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

A tower

AB

leans towards west making an angle

\alpha

with the vertical. The angular elevation of

B

, the top most point of the tower, is

{60}^{o}

as observed from a point

C

due east of

A

at a distance of

10ft

from

A.

If the angular elevation of

B

from a point

D

due east of

C

at a distance of

20ft

from

C

{45}^{o}

, then the value of

2tan \alpha

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

Options

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

Correct answer

C. $\sqrt{3} - 1$

Step-by-step solution

\left(m - n\right)

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

30cot {60}^{o} = 10cot {45}^{o} - 20\cot \left(\dfrac{\pi}{2} + \alpha\right) <

br/>

⇒ 10\sqrt{3} =10 + 20tan \alpha <br/>

⇒ 2tan

\alpha = \sqrt{3} -1

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