1. Math and terminology for future Truckers
Unit 2: Slopes and Gradients
Note: You will need to know how to measure angles for this unit. To review how to measure angles, ask for Unit 1: Measuring Angles
Created by Leecy Wise for Utah State University-Eastern Campus, Blanding, UT, 2014
© Utah State University-Eastern Campus: Blanding, 2014

2. Please use your mouse to click through each slide
Please use your mouse to click through each slide. That will allow animations and quizzes to play correctly. Use the back arrow key on your keyboard or the back arrow icon at the bottom left part of each slide to move to previous slides.
Move your cursor here to use back arrow

3. Road humor
When you are laughing, you are learning, so laugh, laugh, laugh!
Transport Topics: The Newspaper of Trucking and Freight Transportation

4. flashcards
You will work with several new terms in this unit. As always, when learning new terms, create flash cards and go over them many times until you really know the term. Illustrate your cards with images that make sense to you! You can go to any general store, like Walmart, Walgreens, Dollar Store, or other businesses in you area, and buy a stack of 3 X 7 index cards. They can be lined or unlined, depending on what you want. Better yet, buy a box with indexed divisions in alphabetical order!

5. WHAT ABOUT GRADIENTS?
Any student knows about grades. A grade shows how a student progresses along a path that usually goes up from 0 to 100, or 0% to 100%. On a graph below a grade of 89% might look as follows. The student started at 0, as everyone starts at the beginning of the year. Then he went up to 89! The chart represents a gradient that goes from 0 to 100, and the student is nearly at the top.
89%

6. In school, a grade represents progress
In school, a grade represents progress. On the road or in an area where heavy equipment is used, a grade is an incline, a slope, or a rise, which is also called a gradient. You will also hear the term “slope gradient” when measuring how far above level ground a line rises. The image above shows that when you measure a slope, you form a triangle. Then you use a formula to find out the ratio, percentage, or degree of the rise or fall that happens from one point to another.

7. If you are not familiar with how angles operate, complete the unit on angles before taking this unit so that you are very familiar with the concept of angles – how they are formed and how they are measured! Ask your instructor for the Angles Unit. When you are done, come back to practice measuring slopes using what you learned. A D C B F E

8. Truckers and pros who handle heavy equipment must learn to measure the steepness of a slope or gradient. Why? So that they can stay alive and to keep from harming anything around them, including people! One of the top reasons from accidents leading to death among those who work with heavy loads and heavy equipment is failure to measure angles and to know how they affect their carriers.

9. 1. TERMS
To start, make sure that you have the following terms in your flashcard collection!
Grade - the pitch or steepness of a slope such as a hill, road or railway.
Gradient – Another word for grade, used in trucking to describe the steepness of a slope.
Pitch – The amount of steepness or inclination of a grade, gradient or slope.
Slope – In math, slope is the number that describes both the direction and the steepness of a line on a grade or gradient. In simple terms, slope is the change in height over a horizontal distance.

10. As you can see, people use different terms to describe and to assess the amount of inclination on a road or in using heavy equipment. Knowing how to measure inclination or slope is critical to keeping you and others safe! From the image, below, you can see that you can measure gradients by drawing an imaginary right triangle to follow each slope. Notice that the pitch of the first gradient is smaller than that of the second and third gradient.

11. 2. CALCULATING THE PITCH OF A SLOPE
In this unit, we are going to practice calculating the pitch (inclination or gradient) of a slope.
The amount of pitch on slopes can be measured in ratios (X/Y or X:Y), percents (%), and degrees (0). We will practice all of these.
A slope is typically illustrated using three lines:
a horizontal line, representing the run of the slope.
a vertical line, representing the rise,
And a third connecting line that represents the pitch of the slope.

12. a horizontal line (blue), representing the run,
a vertical line (red), representing the rise,
and a third connecting line (olive) that represents the slope.
Click to see animation.

13. The RUN – horizontal line that represents the length of the slope being measured.
The RISE – the vertical line that represents the height of the slope being measured.
The slope – the amount of inclination or pitch of the slope. This line is also called a TANGENT in geometry.
The angle formed when measuring a slope.
Keep filling out those flashcards and test yourself every day on these terms!

14. It will help you to know that once you draw or measure a slope, you form a right triangle to represent the pitch on a slope, you can then determine the degree of pitch that is involved. Amount of pitch – A number that describes the amount of inclination on a slope. That amount can be described as a ratio, percent, or a degree. Road gradients are usually expressed in %.

15. How do we calculate the amount of pitch on a slope
How do we calculate the amount of pitch on a slope? You must use a formula or equation. Memorize the formula. It’s easy and very, very useful! The pitch on a slope is measured using the following formula. What are those little triangles? When you see in a formula, it simply means “change.” Here, it represents the change in vertical and horizontal distances. Don’t let the little symbol throw you. We are not going to use it in our measurements here.
Horizontal distance
Vertical distance
Slope =

16. M = Most people simplify that formula as follows.
Represent the gradient on a slope as “M.” That is what we want to calculate. Why “M?” Mathematicians are not sure. That’s just the way it is! M = gradient or slope.
So start with …
M =

17. 12%
So start with …
M =
Here’s the rest of the formula or equation:
The measurement of the length (run) of any gradient is important as well as the rise from the surface of a slope. This determines the truck and battery capacity and, sometimes, the type of wheel/tire equipment.
RISE
RUN
M =
Make sure you have a flashcard for this formula!
or M = RISE RUN
Horizontal distance
Vertical distance
Slope =

18. In other words… The dividing line between RISE (vertical change) and RUN (horizontal change) always means division. So if you know the rise of a line and the run of a line, you can figure out the amount of inclination or the gradient of a slope by dividing the amount of rise by the amount of run.
Horizontal distance
Vertical distance
Slope =
RISE
RUN
M =
is the same as…

19. RISE
RUN
M =
The RISE is the vertical line showing how far up or down a slope goes. That line starts at the bottom of the slope, at zero angle (00) and moves up, up, up. The rise line can also move down, down, down. In that case, the RISE number would be stated as a negative or minus (-).
The RUN is the length of the line being measured going right or left on a horizontal plane (00) .
RISE (+)
RISE (-)
RUN
RUN
RISE
M =

20. 6
Let’s say that you have a positive rise of 6. Let’s say that you have a run of 6 as well. What is the pitch of the slope? Use the formula. Let’s show those measurements on a graph. 6
RISE
RUN
M = 6
M =
= 1 (6 divided by 6 is 1.)

21. 3. GRAPHING
To understand the amount of pitch (inclination) on a slope, it is very helpful to draw a graph to help you calculate slopes. Graph – a graph is an image created on graph paper, that shows a vertical line and a horizontal line that meet in the middle. (Keep adding to your flashcard collection!) Each line is called an axis. The plural of “axis” is “axes:” one axis; two or more axes. The middle point of the graph, where the lines meet is usually called the origin.
Origin
Axes

22. In graphing, the vertical line going up and down, is labeled “Y” axis
In graphing, the vertical line going up and down, is labeled “Y” axis. It might help to remember this line because the Y has a small vertical line along it’s lower part. The rise will move up or down the Y (vertical axis) The horizontal line on a graph, is labeled “X” axis. Notice that the lines on an “X” don’t go straight vertically or horizontally. They are diagonal, but you can imagine a horizontal line going through the X. Y X X Y
Y axis
X axis

23. Draw and name each of the following axes.

24. Vertical: Y Horizontal: X

25. Let’s plot (calculate the position) of the pitch we described earlier: RISE= 6 and RUN=6. First, count six squares going across (run). Then draw a line going up from where the run ends (rise). To see the pitch, draw a line diagonally to have rise meet run. Click for animation.
Y axis
6 squares rising to meet …
RISE
X axis
6 squares running across
RUN 6
M =
= 1

26. RISE= 6 and RUN=6. To review, first, count six squares going across (run). Draw count the numbers in the rise and draw a slope line from the origin to meet it.
Y axis
X axis
6 squares rising to meet …
6 squares running across 6
M =
= 1

27. Let’s plot another pitch with a RISE= 6 and RUN=4
Let’s plot another pitch with a RISE= 6 and RUN=4. First, count four squares going across (run), and then six squares going up (run). As you can see, M always equals a fraction. Divide the numbers and you have the amount of pitch.
Y axis
6 squares rising to meet …
X axis
4 squares running across 6 4
M =
= Pitch is 1.5

28. Notice that when you draw a line up to show the rise of a slope, you form a right angle. When you draw the slope line, you form a triangle. Sometimes, you’ll see a little square showing the right angle where the rise and run lines meet. Refer to the angles unit where you learned that a right triangle is formed by a horizontal line (run) meeting a vertical line (rise). A right triangle always has a 900 angle where rise meets run. It is usually shown as a little square. When you measure slope, you always form a right triangle.
angle of the slope
right angle

29. How do you know if the line showing the upgrade or the downgrade of a slope? Is the line going up or down? One simple way is to write your name on top of the line. If the letters in your name go down, the number will be negative. It is going down. If the letters on your name are going up, the number will be positive. It is going up! On the road, downhill slopes require more handling than uphill slopes. You gain speed going down, and the greater the speed, the harder it is to control a vehicle!
Sam

30. Watch the following videos to see how you measure pitch on a slope using the formula you were given. When you are done with one video clip, to go to the next video or slide, click anywhere outside the stage. Allow a few seconds for each video to load.

31. http://www. youtube. com/watch
Allow a few seconds for the video to load.

32. Video 2 (23:24 m total, but watch only the first 12:22 minutes

33. Video 3 (5 minutes) http://www.youtube.com/watch?v=zTa0xTu9Yv4

34. 4. EXPRESSING GRADIENTS AS RATIOS
A slope is an incline. It is sometimes called a gradient. The amount of inclination on a slope is called “pitch.” The pitch of a slope is measured by the formula M=RISE/RUN: The amount of pitch on a slope is always found as a ratio. A ratio is simply a comparison between two items. In this case, those two items are RISE and RUN. Ratios can be expressed in different ways. The M = formula expresses ratios as fractions. Fractions are ratios.
RISE
RUN
M =
RISE
RUN
expresses a ratio between RISE and RUN

35. Example: A road exam was taken by twelve (12) people
Example: A road exam was taken by twelve (12) people. Out of those twelve, seven people passed and five failed. Seven out of twelve passed. or 7/12. This ratio can also be expressed as 7:12 or 7 to 12. is a ratio represented as a fraction. Five out of twelve failed. or 5/12 . This is a ratio. It can also be expressed as 5:12 or 5 to 12. The pitch of a slope is always initially expressed as a ratio since the “M=“ formula requires a ratio expressed as a fraction! Once you have the amounts for rise and run, you can then divide them to get a whole number or a decimal. 7 12 7 12 5 12
RISE
RUN
M = 5 12
Example:

36. EXAMPLE:
M = 5 12
5 ÷12 = 0.41
M = 8
8 ÷8 = 1
M = 12 8
12 ÷8 = 1.5

37. Practice measuring the pitch of the positive slopes created by the following information. Draw your graph. Use the numbers along the axes to plot your slope. Apply the formula to find the answers. Express your answers as ratios. Then divide the numbers in the ratio to get a whole number (1) or a decimal (0.6). When you are done, click to check your answers. Turn in the numbers that you plotted on your graph into your instructor.
Rise: 4; Run: 6
Rise 7; Run 7
Rise 3; Run 5
Rise 8; Run 8

38. ANSWERS
Rise: 4; Run: 6 = 4/6 or 4:6 or 4 to ÷ 6 = 0.6 (rounded off)
Rise 7; Run 7 = 7/7 or 7:7 of 7 to ÷ 7 = 1
Rise 3; Run 5 = 3/5 or 3:5 or 3 to ÷ 5 = 0.6
Rise 8; Run 8 = 8/8 or 8:8 or 8 to 8. 8 ÷ 8 = 1

39. Notice that when using a computer keyboard, the division line shown on a fraction is often a slanting line instead of a straight, horizontal line: / It also shows division or a fraction.
Rise: 3; Run: M= 3/6 = 0.5
Rise: 7; Run: M= 7/7 = 1
Rise: 3; Run: M= 3/5 = 0.6
Rise: 8; Run: M= 8/8 = 1
Notice that the measurement of a slope is always shown as a fraction or ratio since the formula is described in terms of rise:run or rise to run.
Once you have a fraction, you can then turn it into a decimal or a whole number, as we have done above. We divided Rise by Run. We could also express the answer as a percentage, as we will practice later in this unit.

40. Which slope is steeper, a 0. 5 slope or a 1 slope
Which slope is steeper, a 0.5 slope or a 1 slope? Plot those slopes and click to check your answers.
Rise: 3; Run: M= 3/6 = 0.5
Rise: 8; Run: M= 8/8 = 1

41. Rise: 8; Run: M= 8/8 = 1
Rise: 3; Run: M= 3/6 = 0.5
0.5 1
As you can see, a slope of 1 is steeper than one of 0.5 when you lay one on top of the other.

42. So far, we have plotted upgrades, with positive numbers.
If a slope is going down (downgrade) it makes sense that the numbers would be negative!
If you have never worked with negative numbers, ask your instructor for resources to help you practice calculating with them. The idea is very logical, so you should be able to pick up those skills very quickly.
Following are two sites that will help you get started.
15/bk7_15i1.htm

43. In the graph below, you can see that the line is going down
In the graph below, you can see that the line is going down. Remember that if you write you name and it goes down, it’s a downgrade.
Let’s measure the pitch of a slope along that downgrade. The rise is up four spaces (in green). It is positive. The run, however, goes to the left four spaces. That means that the run is negative (-4). The slope pitch is -1. Four divided by minus four is -1.
Rise: 4
Run: -4 4 -4
= -1

44. A good rule of thumb to remember – if a line runs to the left or down on a graph, it is negative. If a line runs downhill, it is also negative. What is the ratio of the three slopes shown above?
Rise: 4
Run: -4
Rise: -6
Run: 4
Rise: 4
Run: -4 3 1 2

45. A good rule of thumb to remember – if a line runs to the left or down on a graph, it is negative. If a line runs downhill, it is also negative.
What is the ratio of the three slopes shown above?
1. 4: : :4
Rise: 4
Run: -4
Rise: -6
Run: 4
Rise: 4
Run: -4 3 1 2

46. % 5. EXPRESSING GRADIENTS AS A PERCENT M =
So far, you have practiced describing the pitch of a slope as a ratio. You will usually see the rise of a slope shown on a road sign as a percentage, or percent. How can you interpret the ratio you find as a percent?
RISE
RUN
M =

47. Slope percentage is calculated in much the same way as the pitch expressed as a ratio. (People use the words percent and percentage in the same way now a days.) We will use the term “percent.”
You have practiced converting the RISE/RUN measurements into decimals or whole numbers.
EXAMPLES:
Rise 7; Run 7 = 7/7 or 7:7 or 7 to ÷ 7 = 1
Rise 3; Run 5 = 3/5 or 3:5 or 3 to ÷ 5 = 0.6
That is the first step you take. Convert the RISE/RUN measurements into decimals or whole numbers.
The rest is very easy: multiply your answer by 100, and you have the percent amount of pitch on a slope.

48. Let’s practice converting ratios to percents
Let’s practice converting ratios to percents. Suppose you have a 3 mile rise and a 36 mile run (3/36).
3 mi
36 mi
RISE
RUN
M = 3 36
= 0.083

49. Let’s practice converting ratios to percents
Let’s practice converting ratios to percents. Suppose you have a 3 mile rise and a 36 mile run (3/36). NOTE: To multiply any number by 100, simply move the decimal point two spaces to the right. It’s easy. Click to see the process.
3 mi
36 mi
RISE
RUN
M = 3 36
= 0.083
Now multiply that number by 100.
8.3%

50. Connect the line that runs up (or down) from the beginning of the run to the top of the rise to show the slope. That line is called a tangent in geometry.
tangent
8.3% slope
3 mi
36 mi
RISE
RUN
M = 3 36
= = 8.3%

51. Why do we multiply by 100 to get the percent?
When you work with percents, you are ALWAYS working with 100 as your basic unit. If you want practice using percents, ask your instructor for a unit on that topic.100% always represents a total amount.
If you eat a whole sandwich, you eat 100% of the sandwich. If you eat half a sandwich, you eat 50% of it because 50 is half of 100!
What if you cut the sandwich in four equal parts and eat one of those parts. What percent did you eat?
If you said, 25%, you would be correct! 25% is on fourth part of 100.
50%
25%

52. If you are working with money, think of one dollar as representing 100%. Half of a dollar would be 50 cents, or 50% of the dollar. One fourth, or one quarter of a dollar would be 25 cents, or 25% of the dollar. One tenth of the dollar would be a dime, ten cents or 10% of the dollar. One fifth of a dollar would be a nickel, five cents or 5% of the dollar. One hundredth of the dollar would be one cent or a penny, or 1% of the dollar.
100%
50%
25%
10% 5% 1%

53. What is 100% of any slope? Think about it after you examine the image below with a rise of 6 miles and a run of 6 miles.
6 mi
M=6/6= 1
1 X 100 = 100%

54. When the rise and the run have the same distance, the answer is always one or 100%.
Notice that when you draw the rise and the run of the slope and join the end points, you form a right triangle. Later, you will see that slope that rises 100% forms a 450 angle!
M=6/6= 1
1 X 100 = 100%
6 mi

55. Let’s practice converting ratios to percents.
Find the percent amount of slopes with the following dimensions. Use up to two decimal places (hundredths) in your answers.
TIP: When you get your fraction, simply divide the rise by the run to find the decimal that the fraction represents. Then multiply by 100!
4 rise and 16 run
8 rise and 5 run
9 rise and 9 run
8 rise and 20 run
15 rise and 15 run
When you are done, click to check your answers.

56. Find the percent amount of slopes with the following dimensions
Find the percent amount of slopes with the following dimensions. Use up to two decimal places (hundredths).
4 rise and 16 run = 4/16 = X 100 = 25%
8 rise and 5 run = 8/5 = x 100 = 160%
9 rise and 9 run = 9/9 = X 100 = 100%
8 rise and 20 run = 8/20 = X 100 = 40%
15 rise and 15 run = 15/15 = 1 1 X 100 = 100%
Practice measuring slopes more at
More than 100%!

57. Try it out yourself with a plumb line.
Locate or make a ramp. Find a nice plumb bob or line, or make one with a pointed rock. Drop the line from the top of the ramp to the bottom surface and measure that distance. That is the rise. Run a measuring tape from the point where the plumb meets the bottom surface to the end of the ramp. Measure that distance. That is your run.
rise
run
Finally, apply the M formula and write your ratio. You may go further and divide those numbers to get an amount that represents the pitch of the slope. Now you can find the % and degree of the inclination, as you will learn later in this unit.

58. 6. Finding Unknown Values
Sometimes, you might have to find an unknown value using the slope formula. Let’s say that you know a slope is 3/190, but you don’t know what distances those represent. Let’s say that you know that the hill rises 300 m (meters), but you don’t know the distance of the run. Watch the following video to figure that out. Allow time for the video to load. When you finish watching the video, click outside of the stage to go to the next slide.

59. Allow a few seconds for the video to load.
Allow a few seconds for the video to load.

60. Now It’s your turn
Click on the links to open a set of worksheets. Complete the worksheets and turn them into your instructor. Check answers only after completing the worksheets.
Fractions Review – Review how to simplify fractions and find missing numbers in equivalent fractions. For a complete fractions review, ask your instructor to those units. (from )
Calculating Slopes and Rates of Change – Review ratios and calculate slope pitches, find the missing measurements. (Answers) (From )
Slope of Steps – Solve problems relating to slopes.
Rise Over Run – Practice solving word problems using your slope formula. (Answers with Notes) (from )
Slope measures are usually made in the metric system. It doesn’t matter what system you are using to practice measuring the pitch of slopes. The formula is the same. You will find measurements such as kilometers (km), meters (m), centimeters (cm), and millimeters (ml) in your worksheets. To practice measurements in the metric system, ask your instructor for. those units. You will also work with conversions in the last Measurements Unit.

61. 7. EXPRESSING GRADIENTS AS ANGLES
You have practiced measuring the pitch of slopes using ratios and percentages. Now you are ready to represent the degree of a slope by measuring their angles. How do we measure the degree of pitch of a slope? First let’s identify the angle formed by a slope. NOTE: If you want to review angles, ask your instructor for that unit.
The slope – the amount of inclination or pitch of the slope. This line is also called a TANGENT in geometry.
The angle formed when measuring a slope.

62. You know how to identify the rise and the run of a slope
You know how to identify the rise and the run of a slope. Remember the video: rise up and then run. Rise first (top part of the ratio of fraction) and then run (bottom part of the ratio or fraction.) You also know how to draw a line from the start of the run to the top of the rise. That line is called a TANGENT, and it represents the amount of pitch on the slope.
3 m (meters) RISE
14 m (meters) RUN
3 m (meters) RISE
14 m (meters) RUN

63. Notice the angle that is formed as the tangent drives up to meet the top of the rise. That is the angle of the slope. As you would expect the higher the rise from 00, the greater the angle! Remember that a horizontal line runs along 00, because a flat run has no rise.

64. Notice how the angle increases as the rise increases. Go to http://www
Notice how the angle increases as the rise increases. Go to and play with the triangle represented there. Watch the degrees on angle C change on as you move different points of the triangle. 7m 3m
10m
14m
450 8m
We know that slopes that have the same rise as run form 450 angles and have a 100% slope, as we learned earlier.

65. To measure the angle of a slope, you will need a calculator
To measure the angle of a slope, you will need a calculator. That tool will give you the amount of angle after you input the rise and run information. This is how it works. The tangent represents the amount of pitch that results from the formula M=RISE/RUN. In that sense you could state.. tan C = Add “tan” to your flashcard library. 6m
15m
where Tan stands for tangent. C

66. C = arctan 0.4 = _____ 0 C tan C = C= 6 ÷ 15, or 0.46m
15m
tan C =
C= 6 ÷ 15, or 0.4
Next, to find the degree of pitch on a slope, we need to invert the tan using the formula…
C = arctan 0.4 = _____ 0
That will give you the arctan, which represents the angle you are wanting to define. You will need a calculator to find that.
Arctan represents the opposite of, or inverted tan. On the calculator you would do the following to find that arctan:
Press shift+tan buttons.
Enter the angle.
Press the = button.

67. You may want to go into trigonometry for figure out why to invert the tan and how to get the answer yourself. Here, we are just applying trigonometry in simple, easy ways. (Trigonometry is a branch of math that studies the relationships between lengths and angles of a triangle.)

68. Tan: the tangent line representing the slope on a rise. C 6m
15m
Tan C =
C is 6 ÷ 15, or 0.4
Tan: the tangent line representing the slope on a rise.
Arctan: the opposite of tan, or inverted tan, which is used to measure the angle on a right triangle.

69. Tan C = C = arctan 0.4 = ____0 C = arctan 0.4 = _____ 21.800 C6m
15m
Tan C =
C is 6 ÷ 15 (rise over run), or 0.4 In the slope represented above, the formula for finding the angle is Go to the online calculator, below, and find the angle for the slope above. Click to check your answer.
C = arctan 0.4 = ____0
C = arctan 0.4 = _____
21.800

70. Ask your instructor for a calculator that applies the arctan function, or use the online resource you were given. Find the degree of pitch for the following ratios:
6 RISE, 8 RUN
8 RISE, 13 RUN
4 RISE, 16 RUN
20 RISE, 15 RUN
7 RISE, 7 RUN
When you are done, turn in your work to your instructor.

71. You are never likely to have to get out on the road and measure the degree of slope on the road. However, you must know how to interpret the signs you see that give you information on slopes. That way, you will be able to adapt your speed and gears correctly in order to keep your vehicle and others safe. If you see a sign that warns you of a downhill with an 180 gradient, what does that mean? If you work with heavy equipment, knowing how grade calculations relate to working safely with equipment can keep you alive. Roofers must also measure the pitch on slopes all of the time. The idea is the same . Go to to use a tool to calculate the degree of pitch on a slope.

72. The visual below gives you an idea of that amount of slope represented by different degrees. The bottom line shows a run of 12 inches. The vertical line show different rise measures and the degrees that they represent. A run of 12 in and a rise of 12 in represent a 450 angle, shown at the very top.
Image from

73. You can see a similar representation at the following roofing site: Scroll to the bottom of the Web page to use their pitch calculator. Notice that roofers refer to rise as the height of the building and to run as the width of the building in their calculator. Different strokes for different folks!

74. For a good review of measuring the pitch on slopes, go to the following site. The graphic, below, taken from the site, shows another representation of ratio to percentage, to degree of pitch on slopes. Go to

75. Before going to the next unit, take a practice quiz covering some of what you have practiced in this unit.
Click on the link below. A page will open in your browser with links to two quizzes. When you complete both to your satisfaction, you will be ready for the next unit!
Gradients Quiz

76. Now it’s up to you to practice calculating and interpreting safety limits and regulations relating to road gradients and the use of heavy equipment. Stay safe and don’t overestimate your equipment’s ability to handle pitch.

77. CONGRATULATIONS! Your are ready for the next unit!

78. Math and TERMINOLOGY for future Truckers
This series was produced by Utah State University-Eastern Campus, CDL Program.
All content, with exception of links to online resources, is original and tailored to the needs of students hoping to succeed in earning their Commercial Drivers License.
All images are either original or taken from the following resources:
Utah CDL Handbook
Transport Topics: The Newspaper of Trucking and Freight Transportation-
Utah State University-Eastern Campus, Blanding, UT: All Rights Reserved, 2014
© Utah State University-Eastern Campus: Blanding, 2014