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From the top and bottom of the tower the angle of elevation of

Question

From the top and bottom of the tower the angle of elevation of the top of a cliff with height $400$ m are observed to be $30^{\circ}$ and $60^{\circ}$ .Find the height of the tower.

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Elijah Discussed

From the top and bottom of the tower the angle of elevation of the top of a cliff with height

400

m are observed to be

30^{\circ}

and

60^{\circ}

.Find the height of the tower.

6 mins ago

Discuss this question LIVE

6 mins ago

Text solutionVerified

Let

A E

be the tower

A E = h

Let

B D

be the height of the cliff.

Here

B D = 400

From the figure,

∠ B A D = 60^{\circ}

and

∠ CE D = 30^{\circ}

In right angled triangle

△ A B D,

tan 60^{\circ} = \frac{B D}{A B}

\Rightarrow 3 = \frac{400}{A B}

\Rightarrow A B = \frac{400}{3}

In right angled triangle

△ EC D

tan 30^{\circ} = \frac{D C}{EC}

\Rightarrow \frac{1}{3} = \frac{400 - h}{A B}

since

EC = A B

\Rightarrow \frac{1}{3} = \frac{400 - h}{\frac{400}{3}}

\Rightarrow 400 = 3 (400 - h)

\Rightarrow 3 h = 1200 - 400 = 800

\Rightarrow h = \frac{800}{3} = 266.667

∴

Required height of the tower

= 266.667

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Question Text	From the top and bottom of the tower the angle of elevation of the top of a cliff with height $400$ m are observed to be $30^{\circ}$ and $60^{\circ}$ .Find the height of the tower.
Answer Type	Text solution:1
Upvotes	150