Question from http://www.sgforums.com/forums/2297/topics/331504
A and B are 2 houses, 40 m apart, on the same horizontal line as the foot F of a building TF. The angles of depression of A and B from top of building are 25 deg and 58 deg respectively. Find the possible heights of the building.
*************************
Answer:
There are two different ways for the houses to be placed
Taking the difference of the ground distance,
h / tan 25° - h / tan 58° = 40
h (1 / tan 25° - 1 / tan 58°) = 40
1.5196 h = 40
h = 26.3 m
Taking the summation of the ground distance,
h / tan 25° + h / tan 58° = 40
h (1 / tan 25° + 1 / tan 58°) = 40
2.769 h = 40
h = 14.4 m
