Question

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

• A. $166m$
• B. $178m$
• C. $152m$
• D. $184m$

Answer 1

Answer: (C)

$152m$

Let ${}^{\prime }{h}^{\prime }$ be the height of the balloon.

Now, in $△ACB$

$\Rightarrow \sin 45°=\frac{AB}{AC}=\frac{h}{215}$

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

$\Rightarrow h=\frac{215}{\sqrt{2}}=\frac{215\sqrt{2}}{2}=152m$

Hence, the answer is $152m.$