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2 posts are k meter apart and the height of one is double that

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$2$ posts are $k$ meter apart and the height of one is double that of the other, if from the middle point the line joining their feet. An observer find the angular elevations of their tops to be complementary, then the height ( in meters ) of the shorter post is :

\frac{k}{2 2}

\frac{k}{4}

k 2

\frac{k}{2}

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2

posts are

k

meter apart and the height of one is double that of the other, if from the middle point the line joining their feet. An observer find the angular elevations of their tops to be complementary, then the height ( in meters ) of the shorter post is :

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Text solutionVerified

Let the two posts be

A B = 2 h

metres and

C D = h

metres

BE = EC = \frac{k}{2}

Let

∠ D EC = θ

. Then,

∠ A EB = 9 0^{\circ} - θ

Δ A BE

, we have

\frac{2 h}{k /2} = tan (9 0^{\circ} - θ) = cot θ \Rightarrow \frac{4 h}{k} = cot θ

........(i)
In

Δ D EC

, we have

\frac{h}{k /2} = \frac{2 h}{k} = tan θ

......(ii)
Multiplying (i) and (ii), we get,

\frac{4 h}{k} \times \frac{2 h}{k} = cot θ tan θ

\Rightarrow \frac{8 h ^{2}}{k ^{2}} = 1

\Rightarrow h^{2} = \frac{k ^{2}}{8}

\Rightarrow h = \frac{k}{2 2}

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Question Text	$2$ posts are $k$ meter apart and the height of one is double that of the other, if from the middle point the line joining their feet. An observer find the angular elevations of their tops to be complementary, then the height ( in meters ) of the shorter post is :
Answer Type	Text solution:1
Upvotes	150

2 posts are k meter apart and the height of one is double that of the other, if from the middle point the line joining their feet. An observer find the angular elevations of their tops to be complementary, then the height ( in meters ) of the shorter post is :

Text solutionVerified

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$2$ posts are $k$ meter apart and the height of one is double that of the other, if from the middle point the line joining their feet. An observer find the angular elevations of their tops to be complementary, then the height ( in meters ) of the shorter post is :