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The angle of elevation of the top of a tower is $30 °$ , if the height of the tower is doubled, then the angle of elevation of its top will be:

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tan − 1 13

tan − 1 23

tan − 1 33

tan − 1 43

answer is B.

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Detailed Solution

Given that the angle of elevation of the top of a tower is

30 °

.
Let the original height of the tower is h and the distance of the foot of tower from the point of observation is x. Then according to the given condition,
Question Image

We know,

tanθ = \frac{Perpendicular}{Base}

Here,

tanθ = \frac{AC}{BC}

Then,

tan 30 ° = h x ⇒ h = x tan 30 ° ⇒ h = x × 13 ⇒ h = x 3

So, the new height of the tower is

2 h = 2 × x 3 ⇒ 2 h = 2 x 3

Let the new angle of elevation is

θ

. Then,

tanθ = \frac{2 h}{x}

\Rightarrow tanθ = \frac{2 x}{x \sqrt{3}}

\Rightarrow tanθ = \frac{2}{\sqrt{3}}

\Rightarrow θ = \tan^{- 1} (\frac{2}{\sqrt{3}})

If the angle of elevation of the top of tower is

30 °

, the angle of elevation of the tower when its height is doubled will be

tan − 1 23

.
Therefore, option 2 is correct.

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