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The angles of elevation of the top of a tower from two points distant 30 m and 40 m on either side from the base and in the same straight line with it are complementary. The height of the tower is :

  1. 11.54 m

  2. 23.09 m

  3. 34.64 m

  4. 69.28 m

Heights & Distances

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Answer

The angles of elevation of the top of a tower from two points distant 30 m and 40 m on either side from the base and in the same straight line with it are complementary. The height of the tower is. Volume And Surface Area of solid RSA Mathematics Solutions ICSE Class 10.

Let height of the tower (AB) be h meters.

Let P and Q be two points on either sides of the tower.

In triangle ABP,

⇒tan⁡θ=h30....(1)\Rightarrow \tan \theta = \dfrac{h}{30}….(1)

In triangle ABQ,

⇒tan⁡(90∘−θ)=h40⇒cot⁡θ=h40⇒1tan⁡θ=h40⇒1h30=h40⇒30h=h40⇒h2=1200⇒h=1200⇒h=34.64 m.\Rightarrow \tan (90^{\circ} - \theta) = \dfrac{h}{40} \\[1em] \Rightarrow \cot \theta = \dfrac{h}{40} \\[1em] \Rightarrow \dfrac{1}{\tan \theta} = \dfrac{h}{40} \\[1em] \Rightarrow \dfrac{1}{\dfrac{h}{30}} = \dfrac{h}{40} \\[1em] \Rightarrow \dfrac{30}{h}= \dfrac{h}{40} \\[1em] \Rightarrow h^2 = 1200 \\[1em] \Rightarrow h = \sqrt{1200} \\[1em] \Rightarrow h = 34.64 \text{ m.}

Hence, option 3 is the correct option.

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