1. Angles of Elevation and Angles of Depression

2. Angles of Elevation and Angles of Depression
Definition
Angle of Elevation
= angle between the horizontal line which passes through the eyes of an observer and the straight line which joins the eyes of the observer to the object which is situated above the horizontal line
Object
Angle of elevation
Horizontal line

3. Angles of Elevation and Angles of Depression
Definition
Angle of Depression
= angle between the horizontal line which passes through the eyes of an observer and the straight line which joins the eyes of the observer to the object which is situated below the horizontal line
Horizontal line
Angle of depression
Object

4. Angles of Elevation and Angles of Depression
Solving problems involving the angles of elevation and the angles of depression
At a particular instant, a helicopter is situated at a height of 480 m vertically above a fire engine. The distance of the fire engine from the foot of a control tower is 200 m. The angle of depression of the fire engine from the peak of the control tower is 36° 30'.
Calculate
the height of the control tower,
the angle of elevation of the helicopter from the peak of the control tower.

5. Angles of Elevation and Angles of Depression
Calculate the height of the control tower.
Solution:
In ∆BNM,
tan BMN =
Sketch a diagram using all the given information.
480 m
36° 30' B M J N x
h m
200 m
tan 36° 30' =
h = 200 × tan 36° 30'
= 200 × 0.74
= 148 m
 The height of the control tower is 148 m.

6. Angles of Elevation and Angles of Depression
(b)
Calculate the angle of elevation of the helicopter from the peak of the control tower.
Solution:
480 m
36° 30' B M J N x
h m
200 m
JN = 480 – 148 = 332 m
In ∆JMN, tan x = =
= 1.66
x = 58° 56'
The angle of elevation of the helicopter from the peak of the control tower is 58° 56‘.

7. Angles of Elevation and Angles of Depression
Angle of elevation and the corresponding angle of depression are equal
Horizontal line
Angle of depression
The same
Angle of elevation
Horizontal line

8. The End