Question : The thread of a kite makes an angle of 60° with the horizontal plane. If the length of the thread is 80 m, then the vertical height of the kite will be:
Option 1: $\frac{40}{\sqrt{3}}$ metres
Option 2: $\frac{80}{\sqrt{3}}$ metres
Option 3: $80$ metres
Option 4: $40\sqrt{3}$ metres
Correct Answer: $40\sqrt{3}$ metres
Solution :
AB = Length of thread = 80 metres
BC = The vertical height of the kite
∠BAC = 60°
In $\triangle$ABC,
$\sin 60° = \frac{BC}{AB}$
⇒ $\frac{\sqrt{3}}{2}=\frac{BC}{80}$
$\therefore BC = 40\sqrt{3}$ metres
So, the vertical height of the kite is $40\sqrt{3}$ metres.
Hence, the correct answer is $40\sqrt{3}$ metres.
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