Mathematics Class 10

Question

Two men on the same side of a tall building notice the angle of elevation to the top of

the building to be 30° and 60° respectively. If the height of the building is known to be

h=50m, find the distance (in meters) between the two men.

Answer 1

In the figure, A and B represent the two men and CD the tall building.
tan A = tan 30^o = DC / AC = h / AC; and
tan B = tan 60^o = DC / BC = h / BC.
Now the distance between the men is AB
= x = AC − BC = (h / tan 30^o) − (h / tan 60^o)
= (50√3 ) − (50 / √3 ) = 57.73 m.