1. Solving Right Triangles • Given certain measures in a right triangle, we often want to find the other angle and side measures. This is called solving the triangle. • All of the following examples will use degree measure, so set the mode on your calculator to degree.

2. Example 1: • Solve the given triangle: First, solve for θ. Since the sum of the two acute angles in a right triangle is 90°, we have … c So θis 28°. 7 in a

3. Now solve for c, which is the hypotenuse. The side measured 7 in. is the side adjacent to the given 62° angle. The trigonometric ratio using adjacent and hypotenuse is cosine. c 7 in a

4. The value of c is approximately 14.91 inches. c 7 in a

5. Last, solve for a, which is the side opposite the 62° angle. The side measured 7 in. is the side adjacent to the given 62° angle. The trigonometric ratio using opposite and adjacent is tangent. c 7 in a

6. The value of a is approximately 13.17 inches. c 7 in a

7. Example 2: • Solve the given triangle: First, solve for θ. Since the hypotenuse and the side adjacent to θ are given, use cosine. 84.7 cm b 62.3 cm

8. So θis approximately 42.6°. 84.7 cm b 62.3 cm

9. Now solve for α. Since the sum of the two acute angles in a right triangle is 90°, we have … 84.7 cm Soαis approximately 47.4° b 62.3 cm

10. Last, solve for b, which is the side opposite θ. The side measured 62.3 in. is the side adjacent to θ The trigonometric ratio using opposite and adjacent is tangent. 84.7 cm b 62.3 cm

11. The value of b is approximately 57.3 cm. Note that we could have used the Pythagorean Theorem to solve for side b. 84.7 cm b 62.3 cm