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From the top of a tower 80 metres high, the angles of depressi

Question

From the top of a tower $80$ metres high, the angles of depression of two points $P$ and $Q$ in the same vertical plane with the tower are $4 5^{0}$ and $7 5^{0}$ respectively, $PQ =$

80 (3 + 1)

mts

80 (3 - 1)

mts

160 (3 + 1)

mts

160 (3 - 1)

mts

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From the top of a tower

80

metres high, the angles of depression of two points

P

and

Q

in the same vertical plane with the tower are

4 5^{0}

and

7 5^{0}

respectively,

PQ =

11 mins ago

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11 mins ago

Text solutionVerified

Let the distance of

Q

from tower be

a m

And

PQ = d m

tan 7 5^{0} = \frac{h}{a}

\Rightarrow (2 + 3) = \frac{80}{a}

\Rightarrow a = \frac{80}{( 2 + 3 )}

\Rightarrow tan 4 5^{0} = \frac{h}{d + a}

\Rightarrow d + \frac{80}{( 2 + 3 )} = 80

\Rightarrow d = \frac{80 ( 3 + 1 )}{( 2 + 3}

\Rightarrow d = 80 (3 - 1) m

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Question Text	From the top of a tower $80$ metres high, the angles of depression of two points $P$ and $Q$ in the same vertical plane with the tower are $4 5^{0}$ and $7 5^{0}$ respectively, $PQ =$
Answer Type	Text solution:1
Upvotes	150