Assalamualaikum wbt my dear form 5 students,

As you were being told by me before your school holiday, your homework for this holiday is to make a mind map on topic Angle of Elevation and Depression.

Here are some notes on the topics that might help your for reference. :)

Angle of Elevation and Depression

In the diagram below, AB is the horizontal line. q is the angle of elevation from the observer at A to the object at C .

The angle of depression is the angle between a horizontal line from the observer and the line of sight to an object that is below the horizontal line.

In the diagram below, PQ is the horizontal line. q is the angle of depression from the observer at P to the object at R .

Example:

In the diagram below, AB and CD are two vertical poles on horizontal ground. Draw in the angle of elevation of D from B and the angle of depression of C from B

Solution:

Example:

Two poles on horizontal ground are 60 m apart. The shorter pole is 3 m high. The angle of depression of the top of the shorter pole from the top of the longer pole is 20˚. Sketch a diagram to represent the situation.

Solution:

Step 1 : Draw two vertical lines to represent the shorter pole and the longer pole.

Step 2 : Draw a line from the top of the longer pole to the top of the shorter pole. (This is the line of sight).

Step 3 : Draw a horizontal line to the top of the pole and mark in the angle of depression.

Example:

A man who is 2 m tall stands on horizontal ground 30 m from a tree. The angle of elevation of the top of the tree from his eyes is 28˚. Estimate the height of the tree.

Solution :

Let the height of the tree be h. Sketch a diagram to represent the situation.

tan 28˚ =

h – 2 = 30 tan 28˚

h = (30 ´ 0.5317) + 2 ← tan 28˚ = 0.5317

= 17.951

The height of the tree is approximately 17.95 m