Pearson Malaysia Sdn Bhd

Form 4 Chapter 10: Angles of Elevation and Depression

Pearson Malaysia Sdn Bhd

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

Horizontal line

Angle of elevation

Pearson Malaysia Sdn Bhd

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

Object

Horizontal line

Angle of depression

Pearson Malaysia Sdn Bhd

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

(a) the height of the control tower,

(b) the angle of elevation of the helicopter from the peak of the control tower.

Pearson Malaysia Sdn Bhd

Solution:

480 m36° 30'

B

M

J

Nx

h m

200 m

(a)

h = 200 × tan 36° 30'

In ∆BNM,

tan BMN =

= 200 × 0.74= 148 m

The height of the control tower is 148 m.

Sketch a diagram using all the given information.

Calculate the height of the control tower.

tan 36° 30' =

Pearson Malaysia Sdn Bhd

Solution:

480 m36° 30'

B

M

J

Nx

h m

200 m

(b)

x = 58° 56'

The angle of elevation of the helicopter from the peak of the control tower is 58° 56‘.

JN = 480 – 148 = 332 m

In ∆JMN, tan x =

=

= 1.66

Calculate the angle of elevation of the helicopter from the peak of the control tower.

Pearson Malaysia Sdn Bhd

Horizontal line

Angle of elevation and the corresponding angle of depression are equal

Horizontal line

Angle of depression

Angle of elevation

The same

Pearson Malaysia Sdn Bhd