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NIMCET 2015 Mathematics PYQ — Two towers face each other separated by a distance of . As seen f… | Mathem Solvex | Mathem Solvex

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NIMCET 2015 — Mathematics PYQ

NIMCET | Mathematics | 2015

Two towers face each other separated by a distance of $25\text{m}$ . As seen from the top of the first tower, the angle of depression of the second tower's base is $60^\circ$ and that of the top is $30^\circ$ . The height (in meters) of the second tower is:

Choose the correct answer:

A.
$\frac{50}{\sqrt{3}}$

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(Correct Answer)

B.
$\frac{25}{\sqrt{3}}$

C.
$50$

D.
$25\sqrt{3}$

Correct Answer:
$\frac{50}{\sqrt{3}}$

Explanation

1. Triangle 01 (Base calculation):

In $\triangle ABD$ :

$\tan 60^\circ = \frac{H}{25}$

$\sqrt{3} = \frac{H}{25}$

$H = 25\sqrt{3}$

2. Triangle 02 (Top difference calculation):

In $\triangle ACE$ :

$\tan 30^\circ = \frac{AE}{25}$

$\frac{1}{\sqrt{3}} = \frac{AE}{25}$

$AE = \frac{25}{\sqrt{3}}$

3. Final Solving:

Height of second tower $(h) = H - AE$

$h = 25\sqrt{3} - \frac{25}{\sqrt{3}}$

$h = \frac{25(3) - 25}{\sqrt{3}}$

$h = \frac{75 - 25}{\sqrt{3}}$

$h = \frac{50}{\sqrt{3}}$

Conclusion:

Correct option is (a).

Explanation

1. Triangle 01 (Base calculation):