If the angles of elevation of the top of a tower from three collinear points $\mathrm{A}, \mathrm{B}$ and C , on a line leading to the foot of the tower, are $30^{\circ}, 45^{\circ}$ and $60^{\circ}$ respectively, then the ratio, $\mathrm{AB}: \mathrm{BC}$, is :

JEE Main · 2015 · 04 Apr 2015 · Offline · Heights and Distances

If the angles of elevation of the top of a tower from three collinear points

A, B

and C , on a line leading to the foot of the tower, are

3 0^{\circ}, 4 5^{\circ}

and

6 0^{\circ}

respectively, then the ratio,

AB : BC

, is :

(A) $3 : 2$
(B) $1 : 3$
(C) $2 : 3$
(D) $3 : 1$ ✓ Correct

Answer: (D)

Solution

Let the tower have height

h

. The three elevations fix the foot distances:

tan 3 0^{\circ}

places

A

h 3

tan 4 5^{\circ}

places

B

h

, and

tan 6 0^{\circ}

places

C

\frac{h}{3}

. So

A B = h 3 - h = h (3 - 1)

and

B C = h - \frac{h}{3} = \frac{h ( 3 - 1 )}{3}

. Their ratio is

A B : B C = 3 : 1

JEE Main · 2015 · 04 Apr 2015 · Offline · Single correct option

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