# The angle of elevation of the top of a lighthouse 60 m high, from two points on the ground on its opposite sides are 45° and 60°. What is the distance between these two points?

A. 45 m

B. 30 m

C. 103.8 m

D. 94.6 m

**Answer: Option D **

__Solution(By Examveda Team)__

Let BD be the lighthouse and A and C be the two points on ground.

Then, BD, the height of the lighthouse = 60 m

∠BAD = 45°, ∠BCD = 60°

$$\eqalign{ & \tan {45^ \circ } = \frac{{BD}}{{BA}} \cr & \Rightarrow 1 = \frac{{60}}{{BA}} \cr & \Rightarrow BA = 60\,m\,........\left( {\text{i}} \right) \cr & \tan {60^ \circ } = \frac{{BD}}{{BC}} \cr & \Rightarrow \sqrt 3 = \frac{{60}}{{BC}} \cr & \Rightarrow BC = \frac{{60}}{{\sqrt 3 }} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{60 \times \sqrt 3 }}{{\sqrt 3 \times \sqrt 3 }} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{60\sqrt 3 }}{3} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 20\sqrt 3 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 20 \times 1.73 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 34.6\,m\,..........\left( {{\text{ii}}} \right) \cr} $$

Distance between the two points A and C

= AC = BA + BC

= 60 + 34.6 [∵ Substituted value of BA and BC from (i) and (ii)]

= 94.6 m

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