Question : A kite is flying at a height of 123 m. The thread attached to it is assumed to be stretched straight and makes an angle of 60° with the level ground. The length of the string is (nearest to a whole number):
Option 1: 142 m
Option 2: 140 m
Option 3: 139 m
Option 4: 138 m
Correct Answer: 142 m
Solution :
$\sin\theta = \frac{\text{Perpendicular}}{\text{Hypotenuse}}$
⇒ Hypotenuse = $\frac{\text{Height}}{\text{sin(60°)}}$
= $\frac{\text{123 }}{\text{sin(60°)}}$
= $\frac{\text{123}}{\frac{\sqrt{3}}{2}}$
= $\frac{\text{123 × 2}}{\sqrt{3}}$
= $\frac{425.112}{3}$ = 142 m
Hence, the correct answer is 142 m.
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