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The string of a kite is 100 m long. If the string is in the form of a straight line (there is no slack in the string) and makes an angle of 8° with the level ground such that $sin θ = 815$ then what is the height of the kite?

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53.33m

54m

53m

54.33m

answer is A.

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Detailed Solution

Given that,
The string of a kite = 100m.
The string makes an angle of =

8 °

. The value

sin θ = 815

We use the identity

sin θ = height hypotenuse

We draw the diagram,
Question Image

We apply the sine rule in the right-angle triangle

Δ A B C

sin θ = Height Hypotenuse ⇒ sin θ = AB A C

Substituting

θ = 8 °

and AC=100 in

sin θ = A B A C

sin θ = A B A C ⇒ sin 8 ° = A B 100 ⇒ 815 = A B 100

⇒ A B = 810015 ⇒ A B = 80015 ⇒ A B = 53.33 m

Thus, the height of the kite is 53.33 m.
Therefore the correct option is 1.

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