Trigonometric Ratios

1. Trigonometric Ratios Lesson 9.10

2. Table of Trigonometric Ratios • The table shows decimal approximations of the ratios for their angles. For example, sin 10º ≈ 0.1736 and the tan 52º≈ 1.2799

3. E Find the measure of D to the nearest degree. 20.1 11.2 34º D F • Should you use sin, cosine or tangent? • Sin D = 11.2 20.1 • Sin D ≈ 0.5572 • Use the table to find the number nearest 0.5572 in the sin column. • D ≈ 34º Find the length of DF to the nearest tenth. • Should you use sin, cosine or tangent? • Cos 34º = DF 20.1 • 0.8290 ≈ DF 20.1 • 16.7 ≈ DF

4. Angle of Elevation • If an observer at point P looks upward toward an object at A… • …the angle the line of sight PA makes with the horizontal PH is called the angle of elevation. A P  of elevation H

5. Angle of Depression • If an observer at point P looks downward toward an object at B… • …the angle the line of sight PB makes with the horizontal PH is called the angle of depression. H P  of depression Taco Meat B

6. To an observer on a cliff 360 m above sea level, the angle of depression of a ship is 28º. What is the horizontal distance between the ship and the observer? Draw a picture. By║ lines alt. int.  s  , CSH = 28º What trig. function will you use? Tan 28º = 360 x 0.5316 ≈360 x x = 677 The horizontal distance is about 677 m.