d The top of a 15 meter high tower makes an angle of elevation

# Height and Distance MCQ 1(Height calculation)

Height and Distance MCQ 1 :The top of a 15 meter high tower makes an angle of elevation of 60° with the bottom of an electric pole and angle of elevation of 30° with the top of the pole. What is the height of the electric pole ?

A. 5 meters                b) 8 meters                    c) 10 meters                 d)  12 meters

Solution:

This a problem of two right angled triangles !

i-e

$\triangle ABT and \triangle BTC$

If we consider height of electric pole i-e from from C to D as ‘h’ – then length D to T will be 15-h

i-e

if CD = h then DT = 15-h

From triangle BTC we have,

$\tan 60 = \frac{TC}{BC}=\frac{15}{BC}$

or

$BC=\frac{15}{\sqrt3}$

$\tan30=\frac{TD}{AD}=\frac{15-h}{AD}$

or

$\frac{1}{\sqrt3}=\frac{15-h}{AD}$

or

$AD=\sqrt3(15-h)$

Now we see that ABCD is a rectangle – and in a rectangle opposite sides are equal so,

AD=BC ​$$=\frac{15}{\sqrt3}$$

So, we can say,

$\frac{15}{\sqrt3}=\sqrt3(15-h)$

$15=\sqrt3\times\sqrt3(15-h)$

$15=3(15-h)$

$3h=45-15=30$

$h=10m$

So, the height of the electric pole is 30 meters