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A balloon is connected to a meteorological station by a cable of length $200 m$ , inclined at $60^{o}$ to the horizontal. Find the height of the balloon from the ground. Assume that there is no slack in the cable.

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173.2 m

192.35 m

123.25 m

None of these

answer is A.

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Detailed Solution

It is given that a balloon is connected to a meteorological station by a cable of length

200 m

, inclined at

60^{o}

to the horizontal.
Let

C

be the position of the meteorological station,

B

be the position of the balloon and

CB

be the cable.
Let the height of the balloon from the ground be

AB = h

From the

ΔACB

\frac{AB}{BC} = \sin 60^{\circ}

⇒

\frac{h}{200} = \frac{\sqrt{3}}{2}

⇒

h = 200 \times \frac{\sqrt{3}}{2}

⇒

h = 100 \sqrt{3}

⇒

h = 100 \times 1.732

⇒

h = 173.2

…(since

\sqrt{3} = 1.732

).
Hence, the height of the balloon above the ground is

173.2 m

.
Hence, the correct option is 1.

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