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Lesson 5.2 Apply the tangent ratio Georgia Performance Standards: MM2G2a, MM2G2b, MM2G2c Vocabulary • Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles and the calculations based on these relationships. • A trigonometric ratio is a ratio of the lengths of two sides in a right triangle. • In a right triangle, the ratio of the length of the leg opposite an acute angle to the length of the leg adjacent to the angle is constant for a given angle measure. • This ratio is called the tangent of the angle. Tangent Ratio: • Let triangle ABC be a right triangle with acute angle A. The tangent of angle A (written as tan A) is defined as follows: opposite tan A adjacent A B C BC AC Find the tan of both x and y. opposite 13 tan x 0.1548 adjacent 84 opposite 84 tan y 6.4615 adjacent 13 Guided Practice opposite tan x adjacent Example 2 Find the value of x Use the tangent of an acute angle to find a leg length. Guided Practice opposite tan x adjacent Example 4 Estimate height using tangent What if the angle were 72⁰ ? 72⁰ 72⁰ Homework • Using Tangent Ratios • p.159: 1 – 13

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