A tower leans towards west making an angle α with the vertical. The...

A tower leans towards west making an angle

\alpha

with the vertical. The angular elevation of

B,

the top most point of the tower, is

{75}^{o}

as observed from a point

C

due east of

A

at a distance of

20

units. If the angular elevation of

B

from a point due east of

C

at a distance of

20

units& from

C

{45}^{o},

then

tan \alpha

is equal to A tower leans towards west making an angle α with the vertical. The angular elevation of B, the top most point of the

Options

A $\dfrac{\sqrt{3} + 1}{2}$
B $\dfrac{\sqrt{3} + 1}{\sqrt{3} - 1}$
C $3 - 2\sqrt{3}$
D $\dfrac{\sqrt{3} - 1}{2}$

Correct answer

C. $3 - 2\sqrt{3}$

Step-by-step solution

\left(m – n\right)

theorem, we have
A tower leans towards west making an angle α with the vertical. The angular elevation of B, the top most point of the

40cot {75}^{o} = 20cot {45}^{o} - 20cot

\left(\dfrac{\pi}{2} + \alpha\right)<

br />

⇒ 40\left(2 - \sqrt{3}\right) =

20 + 20tan

\alpha

⇒ tan

\alpha =

3 -

2\sqrt{3}

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