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Q.

A T.V tower stands vertically on a bank of a river. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is $60^{\circ}$ . From a point 20 m away from this point on the same bank, the angle of elevation of the top of the tower is $30^{\circ}$ . Find the height of the tower and the width of the river.

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a

15.03 m

and 8 m

b

17.32 m

and 10 m

c

19.34 m

and 12 m

d

21.36 m

and 14 m

answer is B.

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Detailed Solution

Given,
The Distance CD = 20 m
The Height of the Tower = AB
The width of the River = BC
Question Image

Question Image

Now, in △ABD we have,

\tan 30^{\circ} = \frac{AB}{BD}

\Rightarrow BD = AB \sqrt{3}

Now, in △ABC we have,

\tan 60^{\circ} = \frac{AB}{BC}

\Rightarrow BC = \frac{AB}{\sqrt{3}}

Now,

BD - BC = CD

\Rightarrow AB \sqrt{3} - \frac{AB}{\sqrt{3}} = 20

\Rightarrow 2 AB = 20 \sqrt{3}

\Rightarrow AB = 10 \sqrt{3}

\Rightarrow AB = 17.32 m

So, tower height = 17.32 m
Also,
River width BC

= \frac{10 \sqrt{3}}{\sqrt{3}}

BC

= 10 m

Option 2 is correct.

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