1. Breakout Session #2 Right Triangle Trigonometry
4/25/2018 1:57 AM
Breakout Session #2 Right Triangle Trigonometry
Presented by
Dr. Del Ferster
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3. A quick look at today’s activities
We’ll spend some time on an “INTRO” to trig.
I have a video to show you, in case you are inclined to teach trig to your students.
We’ll work on the TRIG RIVER ACTIVITY
We’ll work on some “test-like” questions
I know that we usually do these first, but I believe that we’ll benefit more by spending some time looking at the basics of trigonometry together. 

4. 3 Basic Trigonometric Functions
SINE
COSINE
TANGENT

5. Represents an unknown angle
Greek Letter q
Prounounced “theta”
Represents an unknown angle

6. Labeling Right Triangles
The most important skill you need right now is the ability to correctly label the sides of a right triangle.
The names of the sides are:
the hypotenuse
the opposite side
the adjacent side

7. Labeling Right Triangles
The hypotenuse is easy to locate because it is always found across from the right angle.
Since this side is across from the right angle, this must be the hypotenuse.
Here is the right angle...

8. Labeling Right Triangles
Before you label the other two sides you must have a reference angle selected.
Lots of books label this as
It can be either of the two acute angles.
In the triangle below, let’s pick angle B as the reference angle. A B C
This will be our reference angle...

9. Labeling Right Triangles
Remember, angle B is our reference angle.
The hypotenuse is side BC because it is across from the right angle. A
B (ref. angle) C
hypotenuse

10. Labeling Right Triangles
Side AC is across from our reference angle B. So it is labeled: opposite. A
B (ref. angle) C
hypotenuse
opposite

11. Labeling Right Triangles
Adjacent means beside or next to
The only side unnamed is side AB. This must be the adjacent side. A
B (ref. angle) C
adjacent
hypotenuse
opposite

12. Labeling Right Triangles
Let’s put it all together.
Given that angle B is the reference angle, here is how you must label the triangle: A
B (ref. angle) C
hypotenuse
adjacent
opposite

13. Labeling Right Triangles
Given the same triangle, how would the sides be labeled if angle C were the reference angle?
Will there be any difference?

14. Labeling Right Triangles
Let’s put it all together.
Given that angle C is the reference angle, here is how you must label the triangle: A B
C (ref. angle)
hypotenuse
opposite
adjacent

15. Labeling Practice
Given that angle X is the reference angle, label all three sides of triangle WXY.
Do this on your own. Click to see the answers when you are ready. W X Y

16. Labeling Practice
How did you do? W X Y
adjacent
opposite
hypotenuse

17. SOH CAH TOA

18. Sample keystroke sequences Sample calculator display Rounded
Using a Calculator
You can use a calculator to approximate the sine, the cosine, and the tangent of 74º. Make sure your calculator is in degree mode. The table shows some sample keystroke sequences accepted by most calculators.
Sample keystroke sequences
Sample calculator display
Rounded
approximation 74 or
sin
Enter
0.9613 74 or
cos
Enter
0.2756 74 or
tan
Enter
3.4874

19. Finding a Side
Using trig functions to find the length of a missing side.

20. tan 71.5° y tan 71.5° y = 50 (tan 71.5°) y = 50 (2.98868)
A surveyor is standing 50 feet from the base of a large tree. The surveyor measures the angle of elevation to the top of the tree as 71.5°. How tall is the tree?
tan 71.5° y
tan 71.5°
71.5°
y = 50 (tan 71.5°) 50
y = 50 ( )

21. 200 60° x cos 60° x (cos 60°) = 200 x X = 400 yards
A person is 200 yards from a river. Rather than walk directly to the river, the person walks along a straight path to the river’s edge at a 60° angle. How far must the person walk to reach the river’s edge?
cos 60°
x (cos 60°) = 200
200
60° x x
X = 400 yards

22. Finding an Angle
Using trig functions to find the measure of one of the acute angles.

23. Redraw the figure and mark on it HYP, OPP, ADJ relative to the unknown angle
Steps to finding the missing angle of a right triangle using trigonometric ratios:
OPP 
5.92 km
2.67 km
ADJ
HYP

24. For the unknown angle choose the correct trig ratio which can be used to set up an equation
Set up the equation
Steps to finding the missing angle of a right triangle using trigonometric ratios:
OPP 
5.92 km
HYP
2.67 km
ADJ

25. Steps to finding the missing angle of a right triangle using trigonometric ratios:
Solve the equation to find the unknown using the inverse of trigonometric ratio.
OPP 
5.92 km
HYP
2.67 km
ADJ

26. Practice Together:
Find, to one decimal place, the unknown angle in the triangle. 
3.1 km
2.1 km

27. YOU DO:
Find, to 1 decimal place, the unknown angle in the given triangle. 
7 m
4 m