Describe angle of depression of an object as observed from a point with the
help of diagram.
Answers
We will now consider some practical applications of trigonometry in the calculation of angles of elevation and angles of depression.
What is angle of elevation?
The angle of elevation is the angle between a horizontal line from the observer and the line of sight to an object that is above the horizontal line.
In the diagram below, AB is the horizontal line. θ is the angle of elevation from the observer at A to the object at C.
angle of elevation
What is angle of depression?
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. θ is the angle of depression from the observer at P to the object at R.
angle of depression
How to define an angle of elevation or an angle of depression?
Find angles of depression and angles of elevation, and the relationship between them.
Angles of elevation and depression are equal.
Show Step-by-step Solutions
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:
angle of elevation and depression example
How to solve word problems that involve angle of elevation or depression?
Step 1: Draw a sketch of the situation.
Step 2: Mark in the given angle of elevation or depression.
Step 3: Use trigonometry to find the required missing length
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.
How to solve word problems involving angles of elevation and angles of depression?
Examples:
1. An observer standing on top of a vertical spots a house in the adjacent valley at an angle of depression of 12°. The cliff is 60m tall. How far is the house from the base of the cliff?