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10.1: The Tangent Ratio 0011 0010 1010 1101 0001 0100 1011 Expectation: G1.3.1: Define the sine, cosine, and tangent of acuteangles in a right triangle as ratios of sides. Solve problems about angles, side lengths, or areas using trigonometric ratios in right triangles. 1 7/7/2017 2 4 10.1: The Tangent Ratio 0011 0010 1010 1101 0001 0100 1011 The length of arc XY of a circle is equal to ⅙ of the circumference of the circle. The length of the arc is 7π inches? What is the radius, in inches, of the circle? 1 7/7/2017 2 4 10.1: The Tangent Ratio Tangent 0011 0010 1010 1101 0001 0100 1011 a. Draw Δ ABC w/ m A=40, m B = 90 and AB=2 b. Draw Δ DEF w/ m D=40, m E = 90 and DE=2.5 c. Draw Δ GHI w/ m G=40, m H = 90 and GH=3 1 7/7/2017 2 4 10.1: The Tangent Ratio Tangent 0011 0010 1010 1101 0001 0100 1011 d. Determine BC, EF and HI e. Compare 7/7/2017 BC EF HI , , AB DE GH 1 2 4 10.1: The Tangent Ratio Tangent Ratio 0011 0010 1010 1101 0001 0100 1011 Defn: In a right triangle with acute angle, A, with a measure of θ (theta), the tangent of A (tan A = tan A = tan θ) is the ratio of the length of the leg opposite A to the length of the leg adjacent to A. 1 7/7/2017 2 4 10.1: The Tangent Ratio opposite Tan θ = adjacent opposite 0011 0010 1010 1101 0001 0100 1011 1 θ adjacent 7/7/2017 2 4 10.1: The Tangent Ratio opposite Tan α = adjacent adjacent 0011 0010 1010 1101 0001 0100 1011 α 1 opposite 7/7/2017 2 4 10.1: The Tangent Ratio Give the tangent of A and B for the triangle below. 0011 0010 1010 1101 0001 0100 1011 A 13 5 B 12 7/7/2017 1 2 4 10.1: The Tangent Ratio Using a Trig Table (page 870) 0011 0010 1010 1101 0001 0100 1011 What is tan θ if: a. θ = 30 b. θ = 75 7/7/2017 1 2 4 10.1: The Tangent Ratio Arc Tangent 0011 0010 1010 1101 0001 0100 1011 The arc tangent tells us the measure of the angle with the given tangent ratio. 1 7/7/2017 2 4 10.1: The Tangent Ratio Arc Tangent 0011 0010 1010 1101 0001 0100 1011 What is θ if: a. tan θ = 1.483 b. tan θ = .176 7/7/2017 1 2 4 10.1: The Tangent Ratio Tangent on a Calculator 0011 0010 1010 1101 0001 0100 1011 TAN -1 TAN tangent θ arc tangent θ 1 2 4 Calculator must be set in degree mode!!!!!! 7/7/2017 10.1: The Tangent Ratio Using your calculator, what is: 0011 0010 1010 1101 0001 0100 1011 tan 23? tan 45? 7/7/2017 1 2 4 10.1: The Tangent Ratio What is the measure of an angle whose tangent ratio is: 0011 0010 1010 1101 0001 0100 1011 .6532 .0175 7/7/2017 1 2 4 10.1: The Tangent Ratio Calculate the measure of A to the nearest tenth of a degree. 0011 0010 1010 1101 0001 0100 1011 B 5 A 7/7/2017 12 1 2 4 C 10.1: The Tangent Ratio Calculate BC below to the nearest hundredth. 0011 0010 1010 1101 0001 0100 1011 B C 7/7/2017 34° 15 A 1 2 4 10.1: The Tangent Ratio Calculate AC below to the nearest hundredth. 0011 0010 1010 1101 0001 0100 1011 B 10 A 18° 7/7/2017 C 1 2 4 10.1: The Tangent Ratio The directions for assembling a pool ladder state that the ladder should be placed at an angle of 75 relative to level ground. If the pool walls are 6 feet tall, which of the 0011 0010following 1010 1101expressions 0001 0100 1011 gives the distance in feet, that the ladder should be placed away from the bottom edge of the pool to comply with the directions? A. B. C. D. E. 6 tan 75 tan 75 6 1 6 tan 75 6 tan 75 tan (6 75°) 7/7/2017 1 Must show work for full credit!!!!! 2 4 10.1: The Tangent Ratio Ice Cream Anyone? 0011 0010 1010 1101 0001 0100 1011 Ben and Jerry are on one side of river and Edy is on the other. Ben is 20 meters directly south of Jerry. Jerry and Edy are directly across the river from each other. 1 7/7/2017 2 4 10.1: The Tangent Ratio Ice Cream Anyone? 0011 0010 1010 1101 0001 0100 1011 If Ben points at Edy and Jerry at the same time, his arms form a 54° angle. How far is it across the river? Round your answer to the nearest tenth of a meter. 1 7/7/2017 2 4 10.1: The Tangent Ratio J E 0011 0010 1010 1101 0001 0100 1011 20 54° B 7/7/2017 1 2 4 10.1: The Tangent Ratio 0011 0010 1010 1101 0001 0100 1011 As shown in the figure below, what is the tangent of angle C? B 5 1 A 7/7/2017 C 1 2 4 10.1: The Tangent Ratio Assignment 0011 0010 1010 1101 0001 0100 1011 pages 635-637, # 13-33 (odds), 35-39 (all) 7/7/2017 1 2 4 10.1: The Tangent Ratio