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

Trigonometric Ratios

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

Ex 2. Sketch a right triangle with acute angle  and find the other five trig ratios of . a) b)

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

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

Special Triangles 1  in degrees  in radians sin  cos  tan  csc  45 30 60 1 2  in degrees  in radians sin  cos  tan  csc  sec  cot  30 45 60

Ex 3. Evaluate the following without a calculator. a) b)

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

Class Work Evaluate the expression without using a calculator. 4. sin 30 csc 30 5.

Find the exact value of x. 6. 7.

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.

Ex 5. Solve the triangle. a) b)

Class Work Solve the triangle. 8. 9.

10. 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?