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+1 vote
1.6k views
in Trigonometry by (47.6k points)
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Two buildings are in front of each other on a road of width 15 metres. From the top of the first building, having a height of 12 metre, the angle of elevation of the top of the second building is 30°. What is the height of the second building?

1 Answer

+2 votes
by (46.9k points)
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Best answer

Let AB and CD represent the heights of the two buildings, and BD represent the width of the road.

Draw seg AM ⊥ seg CD 

Angle of elevation = ∠CAM = 30°

AB = 12m 

BD = 15m 

In \(\Box\)ABDM, 

∠B = ∠D = 90° 

∠M 90° …[segAM ⊥ segCD] 

∠A 90° …[Remaining angle of \(\Box\)ABDM] 

\(\Box\)ABDM is a rectangle …[Each angle is 90°]

∴ The height of the second building is 20.65 m.

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