1. Right Triangle Trigonometry
Objectives:
Evaluate trigonometric functions of acute angles
Use the fundamental trigonometric identities
Use trigonometric functions to model and solve real-life problems

2. Precalculus
4.3 Right Triangle Trigonometry

3. Trigonometric Functions
hyp
Precalculus
opp 
adj
4.3 Right Triangle Trigonometry

4. Precalculus
4.3 Right Triangle Trigonometry

5. Example 1
Precalculus
Evaluate the six trig functions of the angle  shown in the right triangle
sin  =
cos  =
tan  =
csc  =
sec  =
cot  =
4.3 Right Triangle Trigonometry 5 12 13 

6. YOU TRY
Precalculus
Evaluate the six trig functions of the angle  shown in the right triangle
sin  =
cos  =
tan  =
csc  =
sec  =
cot  =
4.3 Right Triangle Trigonometry

7. Example 2 Find cos 𝜃 if tan 𝜃 = 1 4 . Precalculus
4.3 Right Triangle Trigonometry

8. You Try Find sec 𝜃 if sin 𝜃 = 3 2 . Precalculus
4.3 Right Triangle Trigonometry

9. Example 3
Evaluating the following to the nearest hundredths using a calculator:
sin 𝜋 6
cos 120°
tan 45°
Precalculus
csc 63°
sec 2𝜋 3
cot 250°
4.3 Right Triangle Trigonometry

10. Example 4 30° 15 x Find the value of x for the right triangle shown
Precalculus x 15
30°
4.3 Right Triangle Trigonometry

11. Example 5
Solve ∆ABC (i.e. find the measures of all the unknown angles and sides of the triangle).
Precalculus A B C
62° 6 c b
4.3 Right Triangle Trigonometry

12. You Try B c a 30° A C Solve ∆ABC. Precalculus
4.3 Right Triangle Trigonometry

13. Example 6
Find the measure of angle B to the nearest tenth (ONE decimal place ). .
Precalculus A B C 9 15
4.3 Right Triangle Trigonometry

14. You Try
Find the measure of angle A to the nearest hundredths (TWO decimal places ).
Precalculus A B C 12
4.3 Right Triangle Trigonometry 15

15. Example 7
Solve ∆ABC (i.e. find the measures of all the unknown angles and sides of the triangle).
Precalculus A B C 9 c 5
4.3 Right Triangle Trigonometry

16. You Try B 12 A C Solve ∆ABC. Precalculus
4.3 Right Triangle Trigonometry

17. Precalculus
4.3 Right Triangle Trigonometry

18. Precalculus
4.3 Right Triangle Trigonometry

19. Precalculus
4.3 Right Triangle Trigonometry

20. Precalculus
4.3 Right Triangle Trigonometry

21. Precalculus
4.3 Right Triangle Trigonometry

22. Precalculus
4.3 Right Triangle Trigonometry

23. Precalculus
4.3 Right Triangle Trigonometry

24. Precalculus
4.3 Right Triangle Trigonometry

25. Precalculus
4.3 Right Triangle Trigonometry

26. Precalculus
4.3 Right Triangle Trigonometry

27. Victory Lap Find the unknown value: Precalculus
4.3 Right Triangle Trigonometry