1. Lesson 9.10 Trigonometric Ratios
Objective:
After studying this section, you will be able to use trigonometric ratios to solve right triangles.

2. We can solve other triangles that are not specifically
Degrees
Radian Measure
Sin
Cos
Tan 46 1 47 2 48 3 49 4 50 5 51 6 52 7 53 8 54 9 55 10 56 11 57 12 58 13 59 14 60 15 61 16 62 17 63 18 64 19 65 20 66 21 67 22 68 23 69 24 70 25 71 26 72 27 73 28 74 29 75 30 76 31 77 32 78 33 79 34 80 35 81 36 82 37 83 38 84 39 85 40 86 41 87 42 88 43 89 44 90 45
We can solve other triangles that are not specifically
and
We can use a table with the ratios already calculated.

3. For some applications of trigonometry, you need to know the meaning of the angle of elevation and angle of depression.
If an observer at a 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 H A
Angle of elevation

4. If an observes at a 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. P H
Angle of depression B
Note: Don’t forget that an angle of elevation or depression is an angle between a line of sight and the horizontal. DO NOT USE THE VERTICAL.

5. Example 1 Given right triangle DEF a. angle D to the nearest degree
b. e to the nearest tenth E
f = 20.1
d = 11.2 D e F

6. Example 2
To an observer on a cliff 360 m above sea level, the angle of depression of a ship is What is the horizontal distance between the ship and the observer? A C B 28
360 m x

7. Summary
Summarize how you can use trigonometric ratios to solve everyday problems.
Homework:
Worksheet 9.10