(Q12) The angle of elevation of the top of a tower from the foot of the building is 30o and the angle of elevation of the top of the building from the foot of the tower is 60o. What is the ratio of heights of tower and building?

Solution :

60°30°xyd

Let the height of the tower = x m

Let the height of the building = y m

Distance between the tower and building = d m.

Angle of elevation of the top of the tower = 30°.

From the figure

tan 30° =
x
d
1
√
 =
x
d

d = √ x ....(1)

Also tan 60° =
y
d
√ =
y
d
d =
y
√
 ....(2)

From (1) and (2)

√ x =
y
√
x
y
 =
1
√ × √
 =
1

∴ x : y = :

∴ The ratio of heights of tower and building = : .