Two men are on the opposite sides of a tower. They measure the...

Two men are on the opposite sides of a tower. They measure the angles of elevation of the top of the tower as

{45}^{o}

and

{30}^{o}

respectively. If the height of the tower is

40m

, then the distance between the men is Two men are on the opposite sides of a tower. They measure the angles of elevation of the top of the tower as 45 ^ o

Options

A $40m$
B $40\sqrt{3}m$
C $68. 28m$
D $109. 28m$

Correct answer

D. $109. 28m$

Step-by-step solution

From

\Delta{O}_{1}AB, tan {45}^{o} = \dfrac{40}{x} ⇒ x = 40m

From

\Delta{O}_{2}AB, cot {30}^{o} = \dfrac{y}{40}

⇒y = 40\sqrt{3}m

Distance between the men

= 40 + 40\sqrt{3} = 109.28m

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