1. NOTES 9.10
Trigonometric Ratios

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

3. 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 =
Sin D ≈
Use the table to find the number nearest 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
≈ DF
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 = x
≈ x
x = 677
The horizontal distance is about 677 m.