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 . h2m

B . h3m

C . √3hm

D . h√3m

Answer: Option B
:
B

Two towers A And B Are Standing At Some Distance Apart. Fro...

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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