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From a point P on the ground, the angle of elevation of the top of a 10 m tall building and a helicopter, hovering over the top of the building are 30° and 60° respectively. Find the height of the helicopter above the ground.

Heights & Distances

ICSE

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Answer

Let QR be the tall building and S be the point at which helicopter is present.

From a point P on the ground, the angle of elevation of the top of a 10 m tall building and a helicopter, hovering over the top of the building are 30° and 60° respectively. Find the height of the helicopter above the ground. Heights and Distances, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

Considering right angled △PQR, we get

⇒tan 30°=QRPQ⇒tan 30°=10PQ⇒13=10PQ⇒PQ=103\Rightarrow \text{tan 30°} = \dfrac{QR}{PQ} \\[1em] \Rightarrow \text{tan 30°} = \dfrac{10}{PQ} \\[1em] \Rightarrow \dfrac{1}{\sqrt{3}} = \dfrac{10}{PQ} \\[1em] \Rightarrow PQ = 10\sqrt{3}

Now considering right angled △PQS, we get

⇒tan 60°=QSPQ⇒3=QS103⇒QS=103×3⇒QS=30.\Rightarrow \text{tan 60°} = \dfrac{QS}{PQ} \\[1em] \Rightarrow \sqrt{3} = \dfrac{QS}{10\sqrt{3}} \\[1em] \Rightarrow QS = 10\sqrt{3} \times \sqrt{3} \\[1em] \Rightarrow QS = 30.

Hence, the height of helicopter above the ground is 30 m.

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