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At a distance 2h m from the foot of a tower of height h m, the

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At a distance $2 h$ $m$ from the foot of a tower of height $h$ $m$ , the top of the tower and a pole at the top of the tower subtend equal angles. Height of the pole should be

\frac{5 h}{3} m

\frac{4 h}{3} m

\frac{7 h}{5} m

\frac{3 h}{2} m

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At a distance

2 h

m

from the foot of a tower of height

h

m

, the top of the tower and a pole at the top of the tower subtend equal angles. Height of the pole should be

7 mins ago

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7 mins ago

Text solutionVerified

Δ A B D

tan α = \frac{h}{2 h}

\Rightarrow tan α = \frac{1}{2}

Δ A BC

tan 2 α = \frac{h + p}{2 h}

\Rightarrow \frac{2 tan α}{1 - tan ^{2} α} = \frac{h + p}{2 h}

\Rightarrow \frac{2 ( \frac{1}{2} )}{1 - ( \frac{1}{2} ) ^{2}} = \frac{h + p}{2 h}

\Rightarrow \frac{4}{3} = \frac{h + p}{2 h}

\Rightarrow 8 h = 3 h + 3 p

\Rightarrow 5 h = 3 p \Rightarrow p = \frac{5 h}{3} m

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Question Text	At a distance $2 h$ $m$ from the foot of a tower of height $h$ $m$ , the top of the tower and a pole at the top of the tower subtend equal angles. Height of the pole should be
Answer Type	Text solution:1
Upvotes	150