Two buildings are facing each other on either side of a road of width 12m. Form the top of the first building , which is 10m. High, the angle of elevation of the top of the second is `60^@`. What is the height of the second building?

Explanation

Let seg AB and seg CD represent the two building.
Seg BD represents the road. ltbr. Seg AE`bot` seg CD…C-E-D.
`angleCAE` is the angle of elevation.
AB = 10 m, BD = 12 m and `angleCAE = 60^@`.
`squareABDE` is a rectangle
DE = AB = 10 m
AE = BD = 12 m
...(Opposite sides of rectangle are equal )
In right angled `triangle`CEA,
`tan 60^@ = (CE)/(AE)` ....(By definition )
`therefore sqrt(3) = (CE)/(12)` ...(`tan 60^@ = sqrt(3) `)
`therefore CE = 12sqrt(3) m`
CD = CE + ED ...(C-E-D)