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A gas balloon is tied with a $215 m$ long rope with an inclination of $45^{\circ}$ with the horizontal. How high is the balloon?

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166 m

178 m

152 m

184 m

answer is C.

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Detailed Solution

It is given that a gas balloon is tied with a

215 m

long rope with an inclination of

45^{\circ}

with the horizontal.
Let h be the height of the balloon.
Question Image

Now, in

△ ACB

\sin 45 ° = \frac{AB}{AC}

⇒

\sin 45 °

= \frac{h}{215}

⇒

\frac{1}{\sqrt{2}} = \frac{h}{215}

⇒

h = \frac{215}{\sqrt{2}}

⇒

h = \frac{215 \sqrt{2}}{2}

⇒

h = 152 m

Hence, the correct option is 3.

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