JEE Main · 2019 · 09 Apr 2019 · Shift 2 · Heights and Distances

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Two poles standing on a horizontal ground are of heights 5 m and 10 m respectively. The line joining their tops makes an angle of

1 5^{\circ}

with ground. Then the distance (in m) between the poles, is

(A) $\frac{5}{2} (2 + 3)$
(B) $5 (3 + 1)$
(C) $5 (2 + 3)$ ✓ Correct
(D) $10 (3 - 1)$

Answer: (C)

Solution

The tops of the two poles differ in height by

10 - 5 = 5

m, and the line joining them rises at

1 5^{\circ}

over the horizontal gap

x

between the poles, so

tan 1 5^{\circ} = \frac{5}{x}

. Since

tan 1 5^{\circ} = 2 - 3

x = \frac{5}{2 - 3} = \frac{5 ( 2 + 3 )}{( 2 - 3 ) ( 2 + 3 )} = \frac{5 ( 2 + 3 )}{1} = 5 (2 + 3)

JEE Main · 2019 · 09 Apr 2019 · Shift 2 · Single correct option

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