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Height and Distance MCQ 1(Tower height and angle of elevation)


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

drawit diagram 2

i-e

if CD = h then DT = 15-h

From triangle BTC we have,

\[ \tan 60 = \frac{TC}{BC}=\frac{15}{BC} \]

or

\[ BC=\frac{15}{\sqrt3} \]

From triangle ADT we have;

\[ \tan30=\frac{TD}{AD}=\frac{15-h}{AD} \]

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

 

 

 

 

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