1. 4.3 Applications Involving Right Triangles
At the end of this lesson you will understand/apply:
sin and sin-1
cos and cos-1
tan and tan-1
30°
60° A B C
What is the correct term for side AB, opposite right C?
What is the side opposite B?
What is the leg side adjacent to B?
What is the side opposite A?
What is the leg side adjacent to A?

2. Three Trigonometric Ratios
Only for RIGHT triangles!!!!!
SOHCAHTOA or SohCahToa

3. Why? To solve triangles other than 30°-60°-90° or 45°-45°-90°.
Look on page 424 in your textbook at the Table of Trigonometric Ratios.
You have the luxury of using a calculator!
IMPORTANT: Your calculator must be in DEGREE mode.

4. Communicating 1. What happens to sin A as A increases?
2. As A increases, what number is sin A approaching?
3. Can you state/write a generalization similar to above that describes the relationship between the cos A and the measure of A.

5. New Vocabulary A
Angle of elevation: The angle between an upward line of sight and the horizontal. P
of elevation H P H
Angle of depression: The angle between a downward line of sight and the horizontal.
of depression B
IMPORTANT: These angles are between a line of sight and the horizontal. Do NOT use the vertical!

6. Using Trigonometric Ratios to Find a Missing Sidex
57
Find missing side to nearest tenth.
10.8
37 x
Find missing side to nearest tenth. 11

7. Using Trigonometric Ratios to Find a Missing Side (cont.)
Find missing side to nearest tenth. x
32 13

8. Using Trigonometric Ratios to Find a Missing Angle
Find missing angle to nearest tenth.  5 4 13 12

9. Using Trigonometric Ratios to Find a Missing Angle (cont.)
Find missing angle to nearest tenth.
7.7 14

10. Using Trigonometric Ratios to Solve a Word Problem
A boat is pulling a parasailer. The line to the parasail is 800 feet long. The angle between the line and the water is about 25. (a) How high is the parasailer? (b) How far back is the parasailer from the boat?
800
25