1. 13.1 - Right Triangle Trigonometry
Grade Distribution
1st
4th
7th
9th A B C D F
No Show
Range
100+
Avg.
2/24/2019 6:23 AM
Right Triangle Trigonometry

2. Right Triangle Trigonometry
Section 13.1
2/24/2019 6:23 AM
Right Triangle Trigonometry

3. 13.1 - Right Triangle Trigonometry
Basic Information
Trigonometry
Comes from Greek word – Trigonon, which means 3 angles
“Metry” means measure in Greek
Trigonometry Ratios
Sine, Cosine, Tangent, Secant, Cosecant, Cotangent
Types of angles
Acute: Less than 90°
Equilateral: 90°
Obtuse: More than 90° but less than 180°
2/24/2019 6:23 AM
Right Triangle Trigonometry

4. 13.1 - Right Triangle Trigonometry
Right Triangles
hypotenuse
opposite
adjacent
Consider a right triangle, one of whose acute angles is ө
The three sides of a triangle are hypotenuse, opposite, and adjacent side of ө
To determine what is the opposite side, look at ө and extend the line to determine the opposite
2/24/2019 6:23 AM
Right Triangle Trigonometry

5. 13.1 - Right Triangle Trigonometry
Right Triangles
Relationships of Trigonometric Ratios
Sine ө = Cosecant ө =
SIN CSC
Cosine ө = Secant ө =
COS SEC
Tangent ө = Cotangent ө =
TAN COT C O E S
2/24/2019 6:23 AM
Right Triangle Trigonometry

6. Steps in Determining Right Triangles
Apply the Pythagorean Theorem by identifying the missing side if it is a Right Triangle
Apply the Trigonometric Functions if it is NOT a Right Triangle
Use Trigonometry Functions to find what’s needed
2/24/2019 6:23 AM
Right Triangle Trigonometry

7. 13.1 - Right Triangle Trigonometry
Example 1
Solve for x and determine all trig functions of ө 6 x 2
Use the Pythagorean Theorem to find the length of the adjacent side…
a = 62
a2 = 32
2/24/2019 6:23 AM
Right Triangle Trigonometry

8. 13.1 - Right Triangle Trigonometry
Example 1
Solve for x and determine all trig functions of ө 6
4√2 2
Determine the hypotenuse and the opposite by identifying ө
adj = 2 opp = 4√2 hyp = 6
SIN ө= COS ө = TAN ө =
CSC ө = SEC ө = COT ө=
2/24/2019 6:23 AM
Right Triangle Trigonometry

9. 13.1 - Right Triangle Trigonometry
Your Turn
Solve for x and determine all trig functions of ө
√29 2 x
SIN ө= COS ө = TAN ө =
CSC ө = SEC ө = COT ө=
2/24/2019 6:23 AM
Right Triangle Trigonometry

10. 13.1 - Right Triangle Trigonometry
Calculator Usage
If ө is given and need to be applied into the calculator, check the MODE.
If the given is in Degrees, convert it into DEGREE Mode
If the given is in Radians, switch it to RADIAN Mode
Ratios
If it is SIN, COS, or TAN function, type the trigonometric function and the angle measure. Then, press enter.
If it is CSC, SEC, or COT function, you must press the reciprocal function first before plugging it in.
2/24/2019 6:23 AM
Right Triangle Trigonometry

11. 13.1 - Right Triangle Trigonometry
Example 2
Solve for x and if necessary, round to three decimal places.
What is given?
Hypotenuse: 74
Opposite of 30°: x
Adjacent: Unknown
Which of the six trig ratios is best fit for this triangle? (there can be more than one answer)
2/24/2019 6:23 AM
Right Triangle Trigonometry

12. 13.1 - Right Triangle Trigonometry
Example 2
Solve for x and if necessary, round to three decimal places.
2/24/2019 6:23 AM
Right Triangle Trigonometry

13. 13.1 - Right Triangle Trigonometry
Example 3
Solve for x and if necessary, round to three decimal places. 20 x
2/24/2019 6:23 AM
Right Triangle Trigonometry

14. 13.1 - Right Triangle Trigonometry
Your Turn
Solve for x, y, and if necessary, round to three decimal places. x 15 y
2/24/2019 6:23 AM
Right Triangle Trigonometry

15. Angle of Elevation vs. Depression
Angle of Elevation is a measurement above the horizontal line
Angle of Depression is a measurement below the horizontal line
Angle of Elevation
Angle of Depression
2/24/2019 6:23 AM
Right Triangle Trigonometry

16. Steps in Application Problems
Read the problem twice.
Draw a picture, if a picture is not given to you
Identify what is missing
Apply the trigonometric function
Show the equation and label appropriately (points will be deducted for failure to label)
2/24/2019 6:23 AM
Right Triangle Trigonometry

17. 13.1 - Right Triangle Trigonometry
Example 4
A flagpole casts a 60-foot shadow when the angle of elevation is 35° (from the distance). Find the height of the flagpole.
Feet ----
2/24/2019 6:23 AM
Right Triangle Trigonometry

18. 13.1 - Right Triangle Trigonometry
Example 5
Find the distance of a boat from a lighthouse if the lighthouse is 100 feet tall, and the angle of depression is 6°.
2/24/2019 6:23 AM
Right Triangle Trigonometry

19. 13.1 - Right Triangle Trigonometry
Your Turn
A man who is 2 feet tall stands on horizontal ground 30 feet from a tree. The angle of elevation of the top of the tree from his eyes is 28˚. Estimate the height of the tree.
2/24/2019 6:23 AM
Right Triangle Trigonometry

20. 13.1 - Right Triangle Trigonometry
Assignment
Page 856
3-5, 7-27 odd, 32
Round to 3 decimal places for odd
2/24/2019 6:23 AM
Right Triangle Trigonometry