Two buildings are in front of each other on either side of a road of width 10 metres. From the top of the first building, which is 30 metres high, the angle of elevation of the top of the second is 45º. What is the height of the second building ?

3. Two buildings are in front of each other on either side of a road of width 10 metres. From the top of the first building, which is 30 metres high, the angle of elevation of the top of the second is 45º. What is the height of the second building ?

Sol.

Let AB  be the height of the first building, CD be the height of the second building,

∴ AB = 30 m,

BD be the width of the road,

∴ BD = 10 m,

∠ CAE = 45⁰,

□ ABDE is a rectangle,

AB = DE = 30 m [Opposite sides of rectangle]

BD = AE = 10 m

In right angled  ∆CEA,

tan 45⁰ = Opposite side of 45⁰ / Adjacent side of 45⁰

∴ 1 = CE/ AE

∴ 1 = CE/10

∴ CE = 10 m

CD = CE + ED [∵  C - E - D]

∴  CD = 10 + 30

∴  CD = 40 m

∴  The height of second building is 40 m.