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Chapter 9 - Trigonometry. Trigonometry:. tri’gonon - triangle. met’ron - measure. 9-1 The Tangent Ratio. B. 5 (opp). 45 . A. C.
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Trigonometry: tri’gonon - triangle met’ron - measure
B 5 (opp) 45 A C 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. opposite 5 ----------- = ---- = ?? adjacent ?? ?? (adj)
B 2 (opp) 45 A C 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. opposite 2 ----------- = ---- = ?? adjacent ?? ?? (adj)
B opposite A C 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
B adjacent A C opposite length of leg opposite B tangent of B = -------------------------------- length of leg adjacent to B opposite tanB = ----------- adjacent
B 2 2 45 A C What is the tangent of 45? 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.
B ?? 60 A C 2 Look at the trig table on page 731. What is the tangent of 60? All 60 angles have a tangent of 1.7321 (3 ). What is the tangent of 60? opposite ?? tanA = tan60 = ----------- = ---- = ?? adjacent ??
B ?? 60 A C 2 Look at the trig table on page 731. What is the tangent of 30? All 30 angles have a tangent of .5771 (1/3 ). What is the tangent of 30? opposite ?? tanB = tan30 = ----------- = ---- = ?? adjacent ??
B x 54 A C 5 Use your calculator, or the trig table, to determine a missing side of a right triangle. x tan 54 = ---- 5 5 tan 54 = x 5 (1.3763) = x
B 7 x A C 5 Use your calculator, or the trig table, to determine a missing angle of a right triangle. 7 tan x = ---- 5 tan x = 1.4 x = 54.5