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Mathematics

The angle of elevation of the top of a pole from a point on the level ground and 15 m away from the pole is 30°. Find the height of the pole.

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Answer

The angle of elevation of the top of a pole from a point on the level ground and 15 m away from the pole is 30°. Find the height of the pole. Volume And Surface Area of solid RSA Mathematics Solutions ICSE Class 10.

Let AB (h) be the height of the pole. Then,

BC = 15 m , ∠ACB = 30°

In triangle ABC,

We know that,

⇒tan⁡θ=Perpendicularbase⇒tan⁡30°=h15⇒13=h15⇒h=153⇒h=151.732⇒h=8.66 m.\Rightarrow \tan \theta = \dfrac{\text{Perpendicular}}{\text{base}} \\[1em] \Rightarrow \tan 30° = \dfrac{h}{15} \\[1em] \Rightarrow \dfrac{1}{\sqrt3} = \dfrac{h}{15} \\[1em] \Rightarrow h = \dfrac{15}{\sqrt3} \\[1em] \Rightarrow h = \dfrac{15}{1.732}\\[1em] \Rightarrow h = 8.66 \text{ m} .

Hence, height of the pole is 8.66 m.

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