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The angle of elevation of a pillar from a point A on the ground is 45° and from a point B diametrically opposite to A and on the other side of the pillar is 60°. Find the height of the pillar, given that the distance between A and B is 15 m.

Heights & Distances

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Answer

Let the height of pillar (CD) be h meters.

The angle of elevation of a pillar from a point A on the ground is 45° and from a point B diametrically opposite to A and on the other side of the pillar is 60°. Find the height of the pillar, given that the distance between A and B is 15 m. Heights and Distances, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

Considering right angled △ACD, we get

⇒tan 45°=CDAC⇒1=hAC⇒AC=h\Rightarrow \text{tan 45°} = \dfrac{CD}{AC} \\[1em] \Rightarrow 1 = \dfrac{h}{AC} \\[1em] \Rightarrow AC = h

From figure,

BC = AB - AC = (15 - h) meters

Considering right angled △BCD, we get

⇒tan 60°=CDBC⇒3=h15−h⇒3(15−h)=h⇒153−3h=h⇒153=3h+h⇒25.98=2.732h⇒h=25.982.732⇒h=9.51\Rightarrow \text{tan 60°} = \dfrac{CD}{BC} \\[1em] \Rightarrow \sqrt{3} = \dfrac{h}{15 - h} \\[1em] \Rightarrow \sqrt{3}(15 - h) = h \\[1em] \Rightarrow 15\sqrt{3} - \sqrt{3}h = h \\[1em] \Rightarrow 15\sqrt{3} = \sqrt{3}h + h \\[1em] \Rightarrow 25.98 = 2.732h \\[1em] \Rightarrow h = \dfrac{25.98}{2.732} \\[1em] \Rightarrow h = 9.51

Hence, the height of the pillar is 9.51 meters.

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