NOTES 9.10 Trigonometric Ratios

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

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

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

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

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.