1. Chapter 9 - Trigonometry

2. Trigonometry: tri’gonon - triangle met’ron - measure

3. 9-1 The Tangent Ratio

4. In a right triangle,  ABC, the ratio of the length of the leg opposite  A to the length of the leg adjacent to  A is constant, no matter what lengths are chosen for the sides of the triangle. A B C 45  5 (opp) ?? (adj) opposite 5 ----------- = ---- = ?? adjacent ??

5. In a right triangle,  ABC, the ratio of the length of the leg opposite  A to the length of the leg adjacent to  A is constant, no matter what lengths are chosen for the sides of the triangle. A B C 45  2 (opp) ?? (adj) opposite 2 ----------- = ---- = ?? adjacent ??

6. This trigonometric ratio is called the tangent ratio. length of leg opposite  A tangent of  A = -------------------------------- length of leg adjacent to  A opposite tanA = ----------- adjacent A B C opposite adjacent

7. length of leg opposite  B tangent of  B = -------------------------------- length of leg adjacent to  B opposite tanB = ----------- adjacent A B C opposite

8. What is the tangent of 45  ? A B C 45  2 2 opposite 2 tanA = tan45  = ----------- = ---- = ?? adjacent 2 opposite 2 tanB = tan45  = ----------- = ---- = ?? adjacent 2 Look at the trig table on page 731. What is the tangent of 45  ? All 45  angles have a tangent of 1.

9. What is the tangent of 60  ? A B C 60  ?? 2 opposite ?? tanA = tan60  = ----------- = ---- = ?? adjacent ?? Look at the trig table on page 731. What is the tangent of 60  ? All 60  angles have a tangent of 1.7321 (  3 ).

10. What is the tangent of 30  ? A B C 60  ?? 2 opposite ?? tanB = tan30  = ----------- = ---- = ?? adjacent ?? Look at the trig table on page 731. What is the tangent of 30  ? All 30  angles have a tangent of.5771 (1/  3 ).

11. Give the tangent ratio for angles A and B.

12. Use your calculator, or the trig table, to determine a missing side of a right triangle. A B C 54  x 5 x tan 54  = ---- 5 5 tan 54  = x 5 (1.3763) = x

13. Find the value of x to the nearest tenth.

14. Use your calculator, or the trig table, to determine a missing angle of a right triangle. A B C xx 7 5 7 tan x  = ---- 5 tan x  = 1.4 x = 54.5 

15. Find the value of x to the nearest degree.

16. Homework: p. 472 1 - 16, 22, 26, 28