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A boy is flying a kite with a string of length 100 m. If the string is tight and the angle of elevation of the kite is 26° 32', find the height of the kite correct to one decimal place (ignore the height of the boy).

Heights & Distances

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Answer

Suppose boy is at point O and the kite is at point P.

A boy is flying a kite with a string of length 100 m. If the string is tight and the angle of elevation of the kite is 26° 32', find the height of the kite correct to one decimal place (ignore the height of the boy). Heights and Distances, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

Considering △POM,

∠PMO = 90°, ∠POM = 26° 32', OP = 100 m and MP = height of kite.

From △POM, we get

⇒sin 26° 32′=MPOP⇒0.4467=MP100⇒MP=0.4467×100⇒MP=44.67≈44.7.\Rightarrow \text{sin 26° 32}' = \dfrac{MP}{OP} \\[1em] \Rightarrow 0.4467 = \dfrac{MP}{100} \\[1em] \Rightarrow MP = 0.4467 \times 100 \\[1em] \Rightarrow MP = 44.67 \approx 44.7.

Hence, the height of the kite is 44.7 metres.

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