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A person of height 2 m wants to get a fruit which is on a pole of height (103)\Big(\dfrac{10}{3}\Big) m. If he stands at a distance of (43)\Big(\dfrac{4}{\sqrt{3}}\Big) m from the foot of the pole, then the angle at which he should throw the stone so that it hits the fruit is:

  1. 15°

  2. 30°

  3. 45°

  4. 60°

Heights & Distances

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Answer

A person of height 2 m wants to get a fruit which is on a pole of height. Volume And Surface Area of solid RSA Mathematics Solutions ICSE Class 10.

Height of the pole (AE) = 103\dfrac{10}{3} m

Height of the person (CD) = 2 m

AE = AB - BE

= 103−2\dfrac{10}{3} - 2

= 43\dfrac{4}{3} m

Distance of man from pole (BD) = (43)\Big(\dfrac{4}{\sqrt{3}}\Big)

From figure,

CE = BD = (43)\Big(\dfrac{4}{\sqrt{3}}\Big) m

In triangle AEC,

⇒tan⁡θ=AECE⇒tan⁡θ=4343⇒tan⁡θ=13⇒tan⁡θ=tan⁡30∘⇒θ=30∘.\Rightarrow \tan \theta = \dfrac{AE}{CE} \\[1em] \Rightarrow \tan \theta = \dfrac{\dfrac{4}{3}}{\dfrac{4}{\sqrt3}} \\[1em] \Rightarrow \tan \theta = \dfrac{1}{\sqrt3} \\[1em] \Rightarrow \tan \theta = \tan 30^{\circ} \\[1em] \Rightarrow \theta = 30^{\circ}.

Hence, option 2 is the correct option.

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