Chapter 9 - Trigonometry

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

9-1 The Tangent Ratio

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 = ---- = ?? adjacent ??

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 = ---- = ?? adjacent ??

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

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

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.

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 (  3 ).

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 ).

Give the tangent ratio for angles A and B.

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  = tan 54  = x 5 (1.3763) = x

Find the value of x to the nearest tenth.

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

Find the value of x to the nearest degree.

Homework: p , 22, 26, 28