# MATHEMATICS NOTES FORM 2 TOPIC 9: TRIGONOMETRY

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**TRIGONOMETRY**

Do you want to learn the relationships involving lengths and Angles of right-angled triangle? Here, is where you can learn.

Angles of Elevation and Angles of Depression

Demonstrate angles of elevation and angles of depression

**Angle of Elevation**of an Object as seen by an Observer is the angle between the horizontal and the line from the Object to the Observer’s aye (the line of sight). See the figure below for better understanding

The angle of Elevation of the Object from the Observer is α

^{0}.**Angle of depression**of an Object which is below the level of Observer is the angle between the horizontal and the Observer’s line of sight. To have the angle of depression, an Object must be below the Observer’s level. Consider an illustration below:

The angle of depression of the Object from the Object is β

^{0}Problems involving Angles of Elevation and Angles of Depression

Solve Problems involving angles of elevation and angles of depression

Example 5

From the top of a vertical cliff 40 m high, the angle of a depression of an object that is level with the base of the cliff is35

^{0}. How far is the Object from the base of the cliff?Solution

We can represent the given information in diagram as here below:

Angle of depression = 35

^{0}Exercise 1

1. Use trigonometric tables to find the following:

- cos 38.25
^{0} - sin 56.5
^{0} - tan 75
^{0}

**2**. Use trigonometrical tables to find the value of x in the following problems.

- sin x
^{0}= 0.9107 - tan x
^{0}= 0.4621

**3**. Find the height of the tower if it casts a shadow of 30 m long when the angle of elevation of the sun is38

^{0}.

**4**. The Angle of elevation of the top of a tree of one point from east of it and 56 m away from its base is25

^{0}. From another point on west of the tree the Angle of elevation of the top is50

^{0}. Find the distance of the latter point from the base of the tree.

**5**. A ladder of a length 15m leans against a wall and make an angle of30

^{0}with a wall. How far up the wall does it reach?