Two towers A and B are standing at some distance apart. From the top of tower A

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Two towers A and B are standing at some distance apart. From the top of tower A, the angle of depression of the foot of tower B is found to be $30^{\circ}$ . From the top of tower B, the angle of depression of the foot of tower A is found to be $60^{\circ}$ . If the height of tower B is ‘h’ m then the height of tower A in terms of ‘h’ is _____ m

Options:

A .

\frac{h}{2}

m

B .

\frac{h}{3}

m

C .

\sqrt{3} h

m

D .

\frac{h}{\sqrt{3}}

m

Answer: Option B
:
B

Let the height of tower A be = AB = H.

And the height of tower B = CD = h

In triangle ABC

tan $30^{\circ}$ = $\frac{A B}{A C}$ = $\frac{H}{A C}$ ...... (1)

In triangle ADC

tan $60^{\circ}$ = $\frac{C D}{A C}$ = $\frac{h}{A C}$ ...... (2)

Dividing (1) by (2) we get, $\frac{t a n 30^{\circ}}{t a n 60^{\circ}}$ = $\frac{H}{h}$

H= $\frac{h}{3}$

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