Trigonometric RatiosLesson 9.10

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.

1. Should you use sin, cosine or tangent?

2. Sin D = 11.2 20.1

3. Sin D ≈ 0.55724. Use the table to find the

number nearest 0.5572 in the sin column.

5. D ≈ 34º

F

E

D

11.220.1

34º

Find the length of DF to the nearest tenth.

1. Should you use sin, cosine or tangent?

2. Cos 34º = DF 20.1

3. 0.8290 ≈ DF 20.1

4. 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.

P

A

H of elevation

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.

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P

B

H of depression

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? 1.Draw a picture.

2.By║ lines alt. int. s , CSH = 28º

3.What trig. function will you use?

4.Tan 28º = 360 x

5.0.5316 ≈ 360 x

x = 677The horizontal distance is about 677 m.