1. Sec 6.2 Trigonometry of Right Triangles
Objectives:
To define and use the six trigonometric functions as ratios of sides of right triangles.
To solve right triangles using trigonometric ratios.

2. Trigonometric Ratios

3. Ex 1. Find the six trig ratios of the angle .

4. Ex 2. Sketch a right triangle corresponding to the trig function of the acute angle . Use the Pythagorean theorem to find the third side and then find the other 5 trig functions.
a) b)

5. Class Work Find the six trig ratios of the angle .7 6 
Find the six trig ratios of the angle .
a) Find sin  and cos 
b) Find tan  and cot 
c) Find sec  and csc    7 4

6. 3. Sketch a right triangle with acute angle  and find the other five trig ratios of . (use Pythagorean Thm)
a) b)

7. Ex 4. Find the exact value of x.
60 x 21
a) b) x 13
45

8. Find the exact value of x. 5. 6.

9. Solving a Right Triangle
A triangle has six parts—three angles and three sides.
To solve a triangle means to determine all of its parts from the information known about the triangle.
In other words, we determine the lengths of the three sides and the measures of the three angles.

10. Ex 5. Solve the triangle. a)

11. Class Work
Solve the triangle. 8.)

12. Applications Involving Right Triangles.

13. Ex 9. From the top of a 200 ft lighthouse, the angle of depression to a ship in the ocean is 23. How far is the ship from the base of the lighthouse?

14. Ex 10.
A surveyor is standing 115 feet from the base of the Washington Monument. The surveyor measures the angle of elevation to the top of the monument as 78.3. How tall is the Washington Monument?

15. HW #1 Pg. 484 (1-21, 29, 31) odd