1. Lesson 5.2 Apply the tangent ratio Georgia Performance Standards: MM2G2a, MM2G2b, MM2G2c

2. 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.

3. 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: A B C

4. Find the tan of both x and y.

5. Guided Practice

6. Example 2 Find the value of x Use the tangent of an acute angle to find a leg length.

7. Guided Practice

8. Example 4 Estimate height using tangent

9. What if the angle were 72⁰ ? 72⁰