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From two points A and B on the same side of a building, the angles of elevation of the top of the building are 30° and 60° respectively. If the height of the building is 10 m, find the distance between A and B correct to two decimal places.

Heights & Distances

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Answer

From figure,

From two points A and B on the same side of a building, the angles of elevation of the top of the building are 30° and 60° respectively. If the height of the building is 10 m, find the distance between A and B correct to two decimal places. Heights and Distances, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

Considering right angled △ACD, we get

⇒tan 30°=CDAC⇒13=10AC⇒AC=10×3=17.32\Rightarrow \text{tan 30°} = \dfrac{CD}{AC} \\[1em] \Rightarrow \dfrac{1}{\sqrt{3}} = \dfrac{10}{AC} \\[1em] \Rightarrow AC = 10 \times \sqrt{3} = 17.32

Considering right angled △BCD, we get

⇒tan 60°=CDBC⇒3=10BC⇒BC=103⇒BC=5.77\Rightarrow \text{tan 60°} = \dfrac{CD}{BC} \\[1em] \Rightarrow \sqrt{3} = \dfrac{10}{BC} \\[1em] \Rightarrow BC = \dfrac{10}{\sqrt{3}} \\[1em] \Rightarrow BC = 5.77

AB = AC - BC = 17.32 - 5.77 = 11.55 meters.

Hence, the distance between A and B = 11.55 meters.

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