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The length of a string between a kite and a point on the ground is 90 m. The string makes an angle of 60° with the level ground. If there is no slack in the string, the height of the kite is:

  1. 45345\sqrt{3} m

  2. 45 m

  3. 90390\sqrt{3} m

  4. 180 m

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Answer

The length of a string between a kite and a point on the ground is 90 m. The string makes an angle of 60° with the level ground. If there is no slack in the string, the height of the kite is: Volume And Surface Area of solid RSA Mathematics Solutions ICSE Class 10.

Length of string (AC) = 90 m

Let the height of the kite (AB) = h

The angle the string makes with the ground is 60°.

⇒sin⁡θ=Perpendicularhypotenuse⇒sin⁡60∘=h90⇒32=h90⇒32×90=h⇒h=453 m.\Rightarrow \sin \theta = \dfrac{\text{Perpendicular}}{\text{hypotenuse}} \\[1em] \Rightarrow \sin 60^{\circ} = \dfrac{h}{90} \\[1em] \Rightarrow \dfrac{\sqrt3}{2} = \dfrac{h}{90} \\[1em] \Rightarrow \dfrac{\sqrt3}{2} \times 90 = h \\[1em] \Rightarrow h = 45\sqrt3 \text{ m}.

Hence, option 1 is the correct option.

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