1. © 2010 Pearson Prentice Hall. All rights reserved. CHAPTER 10 Geometry

2. © 2010 Pearson Prentice Hall. All rights reserved. 2 10.6 Right Triangle Trigonometry

3. © 2010 Pearson Prentice Hall. All rights reserved. Objectives 1.Use the lengths of the sides of a right triangle to find trigonometric ratios. 2.Use trigonometric ratios to find missing parts of right triangles. 3.Use trigonometric ratios to solve applied problems. 3

4. © 2010 Pearson Prentice Hall. All rights reserved. Ratios in Right Triangles Trigonometry means measurement of triangles. Trigonometric Ratios: Let A represent an acute angle of a right triangle, with right angle, C, shown here. 4

5. © 2010 Pearson Prentice Hall. All rights reserved. Ratios in Right Triangles For angle A, the trigonometric ratios are defined as follows: 5

6. © 2010 Pearson Prentice Hall. All rights reserved. Example 1: Becoming Familiar with The Trigonometric Ratios Find the sine, cosine, and tangent of A. Solution: Using the Pythagorean Theorem, find the measure of the hypotenuse c. Now apply the trigonometric ratios: 6

7. © 2010 Pearson Prentice Hall. All rights reserved. Example 2: Finding a Missing Leg of a Right Triangle Find a in the right triangle Solution: Because we have a known angle, 40°, with a known tangent ratio, and an unknown opposite side, “a,” and a known adjacent side, 150 cm, we can use the tangent ratio. tan 40° = a = 150 tan 40° ≈ 126 cm 7

8. © 2010 Pearson Prentice Hall. All rights reserved. Applications of the Trigonometric Ratios Angle of elevation: Angle formed by a horizontal line and the line of sight to an object that is above the horizontal line. Angle of depression: Angle formed by a horizontal line and the line of sight to an object that is below the horizontal line. 8

9. © 2010 Pearson Prentice Hall. All rights reserved. Example 4: Problem Solving using an Angle of Elevation Find the approximate height of this tower. Solution: We have a right triangle with a known angle, 57.2°, an unknown opposite side, and a known adjacent side, 125 ft. Using the tangent ratio: tan 57.2° = a = 125 tan 57.2° ≈ 194 feet 9

10. © 2010 Pearson Prentice Hall. All rights reserved. Example 5: Determining the Angle of Elevation A building that is 21 meters tall casts a shadow 25 meters long. Find the angle of elevation of the sun. Solution: We are asked to find m  A. 10

11. © 2010 Pearson Prentice Hall. All rights reserved. Example 5 continued Use the inverse tangent key The display should show approximately 40. Thus the angle of elevation of the sun is approximately 40°. 11