Question

From a point on the ground, the angles of elevation of the bottom and the top of a tower fixed at the top of a 20m high building are 45 degree and 60 degree respectively. Find the height of the tower.

Answer 1

given that 
dc is the height of the tower = x
ab is the distance between the observer and the building 
the angle of elevation is 45 and 60
from the Δabc

tan45 = bc/ab
1= 20/ab
ab = 20m

from the Δabd
tan60 = bd/ab
√3 = 20+x/20
x = 20√3 - 20
x  = 34.64 -20
x = 14.64m
the hight of the tower is 14.64m