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Question: If the angle of elevation of the top of a tower at a distance 500 m from its foot is \(30 ^ { \circ ...

If the angle of elevation of the top of a tower at a distance 500 m from its foot is 30∘30 ^ { \circ }, then height of the tower is

A

13\frac { 1 } { \sqrt { 3 } }

B

5003\frac { 500 } { \sqrt { 3 } }

C

3\sqrt { 3 }

D

1500\frac { 1 } { 500 }

Answer

5003\frac { 500 } { \sqrt { 3 } }

Explanation

Solution

Let the height be h∴tan⁡30∘=h500⇒h=5003\therefore \tan 30 ^ { \circ } = \frac { h } { 500 } \Rightarrow h = \frac { 500 } { \sqrt { 3 } }