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Mathematics

If the length of the string of a kite flying in the sky is twice the height of the kite from the ground, then the angle of elevation of the kite is:

  1. 30°

  2. 45°

  3. 60°

  4. none of these

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Answer

If the length of the string of a kite flying in the sky is twice the height of the kite from the ground, then the angle of elevation of the kite is: Volume And Surface Area of solid RSA Mathematics Solutions ICSE Class 10.

Let the height of kite (AC) be h.

Length of string (AB) = 2h

In triangle ABC,

⇒sin⁡θ=Perpendicularhypotenuse⇒sin⁡θ=h2h⇒sin⁡θ=12⇒sin⁡θ=sin⁡30∘⇒θ=30∘.\Rightarrow \sin \theta = \dfrac{\text{Perpendicular}}{\text{hypotenuse}} \\[1em] \Rightarrow \sin \theta = \dfrac{h}{2h} \\[1em] \Rightarrow \sin \theta = \dfrac{1}{2} \\[1em] \Rightarrow \sin \theta = \sin 30^{\circ} \\[1em] \Rightarrow \theta = 30^{\circ}.

Hence, option 1 is the correct option.

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