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The angle of depression of two post P and Q at a distance of 2

Question

The angle of depression of two post $P$ and $Q$ at a distance of $2$ meter on the same side of a road from a balloon $(B)$ vertically over the road are observed to be $4 5^{\circ}$ and $6 0^{\circ}$ . What is the height of the balloon?

3 - 3

3 - 1

3 + 3

3 + 1

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Levi Discussed

The angle of depression of two post

P

and

Q

at a distance of

2

meter on the same side of a road from a balloon

(B)

vertically over the road are observed to be

4 5^{\circ}

and

6 0^{\circ}

. What is the height of the balloon?

9 mins ago

Discuss this question LIVE

9 mins ago

Text solutionVerified

let the height of the balloon be

h

and the point on ground be S

△ PBS

tan 45 = \frac{BS}{PS}

BS = PS = h

△ QBS

tan 60 = \frac{BS}{QS}

BS = QS 3

QS = \frac{h}{3}

Now,

PS - QS = 2

h - \frac{h}{3} = 2

h = \frac{2 3}{3 - 1}

h = \frac{2 3 ( 3 + 1 )}{3 - 1}

(Rationalising)

h = 3 + 3

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Question Text	The angle of depression of two post $P$ and $Q$ at a distance of $2$ meter on the same side of a road from a balloon $(B)$ vertically over the road are observed to be $4 5^{\circ}$ and $6 0^{\circ}$ . What is the height of the balloon?
Answer Type	Text solution:1
Upvotes	150