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The angles of elevation of the top of a tower, 40 m high, from two points on the level ground on its opposite sides are 45° and 60°. The distance between the two points in nearest metres is :

  1. 60 m

  2. 61 m

  3. 62 m

  4. 63 m

Heights & Distances

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Answer

The angles of elevation of the top of a tower, 40 m high, from two points on the level ground on its opposite sides are 45° and 60°. The distance between the two points in nearest metres is. Volume And Surface Area of solid RSA Mathematics Solutions ICSE Class 10.

Let AB be the height of tower = 40 m

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

In triangle ABP,

⇒tan⁡45∘=ABBP⇒1=40BP⇒BP=40 m.\Rightarrow \tan 45^\circ = \dfrac{AB}{BP} \\[1em] \Rightarrow 1 = \dfrac{40}{BP} \\[1em] \Rightarrow BP = 40 \text{ m}.

In triangle ABQ,

⇒tan⁡60∘=ABBQ⇒3=40BQ⇒BQ=403⇒BQ=23.09 m.\Rightarrow \tan 60^\circ = \dfrac{AB}{BQ} \\[1em] \Rightarrow \sqrt3 = \dfrac{40}{BQ} \\[1em] \Rightarrow BQ = \dfrac{40}{\sqrt3} \\[1em] \Rightarrow BQ = 23.09 \text{ m}.

Distance between the two points = BP + BQ

= 40 + 23.09

= 63.09 = 63 m.

Hence, option 4 is the correct option.

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