KnowledgeBoat Logo

Mathematics

From the top of a cliff 92 m high, the angle of depression of a buoy is 20°. Calculate to the nearest metre, the distance of the buoy from the foot of the cliff.

Heights & Distances

26 Likes

Answer

Let MP be the cliff and O be the buoy.

From the top of a cliff 92 m high, the angle of depression of a buoy is 20°. Calculate to the nearest metre, the distance of the buoy from the foot of the cliff. Heights and Distances, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

From figure,

Given angle of depression of a buoy is 20°.

∴ ∠POM = ∠OPN = 20° (Alternate angles are equal).

In △POM, ∠PMO = 90°.

From △POM, we get

⇒tan 20°=PMOM⇒0.3640=92OM⇒OM=920.3640⇒OM=252.74≈253\Rightarrow \text{tan 20°} = \dfrac{PM}{OM} \\[1em] \Rightarrow 0.3640 = \dfrac{92}{OM} \\[1em] \Rightarrow OM = \dfrac{92}{0.3640} \\[1em] \Rightarrow OM = 252.74 \approx 253

Hence, the distance of buoy from the foot of cliff is 253 metres.

Answered By

11 Likes

Related Questions