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Mathematics

A kite is attached to a string. Find the length of the string, when the height of the kite is 60 m and the string makes an angle 30° with the ground.

Heights & Distances

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Answer

Let AC be the string and A be the position of kite.

A kite is attached to a string. Find the length of the string, when the height of the kite is 60 m and the string makes an angle 30° with the ground. Heights and Distances, Concise Mathematics Solutions ICSE Class 10.

From figure,

In △ABC,

sin 30°=PerpendicularHypotenuse12=ABACAC=2ABAC=2×60=120m.\text{sin 30°} = \dfrac{\text{Perpendicular}}{\text{Hypotenuse}} \\[1em] \Rightarrow \dfrac{1}{2} = \dfrac{AB}{AC} \\[1em] \Rightarrow AC = 2AB \\[1em] \Rightarrow AC = 2 \times 60 = 120 m.

Hence, the length of the rope is 120 m.

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