Question : A kite is flying in the sky. The length of the string between a point on the ground and a kite is 420 metres. The angle of elevation of a string with the ground is 30°. Assuming that there is no slack in the string, then what is the height (in meters) of the kite?
Option 1: $210$
Option 2: $140\sqrt3$
Option 3: $210\sqrt3$
Option 4: $150$
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Correct Answer: $210$
Solution :
Given: The length of the string is 420 metres and the angle of elevation of a string with the ground is 30°.
$\sin\theta = \frac{\text{Perpendicular}}{\text{Hypotenuse}}$
$⇒\sin 30° = \frac{AB}{420}$
$⇒\frac{1}{2} = \frac{AB}{420}$
$\therefore AB = \frac{420}{2} = 210$ m
Hence, the correct answer is $210$.
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