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There are two temples, one on each bank of a river just opposi

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There are two temples, one on each bank of a river just opposite to each other. One temple is $50$ m. high $A S$ observed from the top of this temple, the angle of depression of the top and foot of other temple are $3 0^{\circ}$ and $4 5^{\circ}$ respectively. Find the width of the river and height of the other temple.

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There are two temples, one on each bank of a river just opposite to each other. One temple is

50

m. high

A S

observed from the top of this temple, the angle of depression of the top and foot of other temple are

3 0^{\circ}

and

4 5^{\circ}

respectively. Find the width of the river and height of the other temple.

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Text solutionVerified

Given BC

= 50

∠ B A C = 4 5^{o}

∠ E D C = 30

A D = h

'm'

Now In ABC,

tan 4 5^{o} = \frac{BC}{A B} = \frac{50}{A B}

A B = \frac{50}{1} = 50 m

Width of river in AB

= 50

Now In

Δ D EC

tan 30 = \frac{CE}{E D} = \frac{50 - h}{A B} = \frac{50 - h}{50}

\frac{1}{3} = 1 - \frac{h}{50}

\frac{h}{50} = 1 - \frac{1}{3}

\Rightarrow h = \frac{50}{3} (3 - 1)

and height of other temple is

\frac{50}{3} (3 - 1)

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Question Text	There are two temples, one on each bank of a river just opposite to each other. One temple is $50$ m. high $A S$ observed from the top of this temple, the angle of depression of the top and foot of other temple are $3 0^{\circ}$ and $4 5^{\circ}$ respectively. Find the width of the river and height of the other temple.
Answer Type	Text solution:1
Upvotes	150