Question

The angle of elevation of the top of the spire from the foot of a building is 60°.The angle of depression of the top of the building from the top of the spire is 47.7°.Given that the height is 15 metres, calculate to one decimal place:
(a)the distance between the spire and the building(4marks)
(b)The difference in height between the spire and the building(2marks)
(c)The height of the spire(2marks)
(d)The angle of depression of the spire from the top of the building(2marks)

Answer 1

when you say "the height is 15 m" I assume you mean the height of the building, since you later ask for the height of the spire. SO, if we let
h = height of spire
x = distance between
Then things are pretty straightforward.
h/x = tan60°
(h-15)/x = tan47.7°
eliminate x, and you have
h/tan60° = (h-15)/tan47.7°
That gives you
h = 41.03m
x = 23.69m
Now the questions can easily be answered. Post your work if you get stuck.