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A man standing on a horizontal plane, observations the angle o

Question

A man standing on a horizontal plane, observations the angle of elevation of the top of a tower to be $α$ . After walking a distance equal to double the height of the tower, the angle of elevation becomes $2 α$ , then $α$ is -

\frac{π}{8}

\frac{π}{12}

\frac{π}{6}

\frac{π}{2}

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A man standing on a horizontal plane, observations the angle of elevation of the top of a tower to be

α

. After walking a distance equal to double the height of the tower, the angle of elevation becomes

2 α

, then

α

is -

6 mins ago

Discuss this question LIVE

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Text solutionVerified

tan 2 α = \frac{2 tan α}{1 - tan ^{2} α}

\frac{h}{x - 2 h} = \frac{2 h / x}{1 - ( \frac{h}{x} ) ^{2}}

\frac{h}{x - 2 h} = \frac{2 k}{x ( \frac{x ^{2} - h ^{2}}{x ^{2}} )}

\frac{x ^{2} - h ^{2}}{x} = 2 x - 4 h

x^{2} - h^{2} = 2 x^{2} - 4 h x

x^{2} + h^{2} - 4 h x = 0

x^{2} - 4 h x + h^{2} = 0

x = \frac{4 h \pm 12 h ^{2}}{2} = h (2 \pm 3)

x

should be greater than

2 h

x = (2 + 3)

tan α = \frac{h}{x} = \frac{1}{2 + 3}

α = \frac{π}{12}

B

is correct.

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Question Text	A man standing on a horizontal plane, observations the angle of elevation of the top of a tower to be $α$ . After walking a distance equal to double the height of the tower, the angle of elevation becomes $2 α$ , then $α$ is -
Answer Type	Text solution:1
Upvotes	150