Question

In the given diagram,AB represents a vertical pole and CD represents a 40 m high tower both of which are standing on the same horizontal plane.From the top of the tower,the angles of depression of the top and the foot of the pole are 24 degrees,30 inches and 48 degrees,30 inches respectively.calculate
(i) the horizontal distance between the pole and the tower
(ii) the height of the pole

Answer 1

Tough to figure out from the "non-given" diagram.
let DB, the horizontal distance be x.
angle ADB = 48 degrees, 30 minutes (not inches!)
= 48.5°
so tan 48.5 = 40/x
x = 40/tan48.5 = 35.39 m

from C, draw a horizontal to meet AB at E
tan 24.5 = AE/x
AE = xtan24.5 = 16.13 m

so height of pole = BE = 40-16.128 = 23.87 m