A stationary balloon is observed from three points A, B and C on...

A stationary balloon is observed from three points

A, B

and

C

on the plane ground and is found that its angle of elevation from each point is

{60}^{o}.

∠ABC = {30}^{o}

and

AC = 5

meters, then the height of the balloon from the ground is A stationary balloon is observed from three points A, B and C on the plane ground and is found that its angle of

A stationary balloon is observed from three points A, B and C on the plane ground and is found that its angle of

Options

A $5\sqrt{3}$ meters
B $\dfrac{5}{4}\sqrt{3}$ meters
C $\dfrac{5}{\sqrt{3}}$ meters
D $\dfrac{5}{4\sqrt{3}}$ meters

Correct answer

A. $5\sqrt{3}$ meters

Step-by-step solution

Let,&

PQ

be vertical with height~

h

~meters& and at its end

Q

there is a balloon and

P

is on the ground

⇒ PA = PB = PC = hcot {60}^{o} = \dfrac{h}{3}

∴P is the circumcentre of

\Delta ABC

and its circumradius \left(R\right) = \dfrac{h}{\sqrt{3}}

\Delta ABC

2R = \dfrac{5}{sin {30}^{o}} ⇒ 2\dfrac{h}{3} = \dfrac{5}{\sin 3{0}^{o}}

∴ h = 5\sqrt{3}

meters.

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