8/28/ : The Tangent Ratio 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.

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? 8/28/ : The Tangent Ratio

8/28/ : The Tangent Ratio Tangent 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

8/28/ : The Tangent Ratio Tangent d. Determine BC, EF and HI e. Compare

8/28/ : The Tangent Ratio Tangent Ratio 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.

8/28/ : The Tangent Ratio θ opposite adjacent Tan θ = opposite adjacent

8/28/ : The Tangent Ratio α adjacent opposite Tan α = opposite adjacent

8/28/ : The Tangent Ratio 5 A13 12 B Give the tangent of  A and  B for the triangle below.

8/28/ : The Tangent Ratio Using a Trig Table (page 870) What is tan θ if: a. θ = 30 b. θ = 75

8/28/ : The Tangent Ratio Arc Tangent The arc tangent tells us the measure of the angle with the given tangent ratio.

8/28/ : The Tangent Ratio Arc Tangent What is θ if: a. tan θ = b. tan θ =.176

8/28/ : The Tangent Ratio Tangent on a Calculator TAN TAN -1 tangent θ arc tangent θ Calculator must be set in degree mode!!!!!!

8/28/ : The Tangent Ratio Using your calculator, what is: tan 23? tan 45?

8/28/ : The Tangent Ratio What is the measure of an angle whose tangent ratio is:

8/28/ : The Tangent Ratio Calculate the measure of  A to the nearest tenth of a degree. A12 5 C B

8/28/ : The Tangent Ratio Calculate BC below to the nearest hundredth. B C A 34° 15

8/28/ : The Tangent Ratio Calculate AC below to the nearest hundredth. A C B 18° 10

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 following expressions 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.6 tan 75 E.tan (6  75°) 8/28/ : The Tangent Ratio Must show work for full credit!!!!!

8/28/ : The Tangent Ratio Ice Cream Anyone? 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.

8/28/ : The Tangent Ratio Ice Cream Anyone? 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.

8/28/ : The Tangent Ratio J B E 54° 20

As shown in the figure below, what is the tangent of angle C? 8/28/ : The Tangent Ratio A 1 B C 5

8/28/ : The Tangent Ratio pages , # (odds), (all) Assignment