a surveyor measures the angle of elevation of the top
of a perpendicular building as 19 degrees. He moves
120m nearer the building and finds the angle of
elevation is now 47 degrees. Determine the height of
the building.
y is the height of the building
x is the distance from the building for the first measurement
(x - 120) is the distance for the second measurement
angle A is 19 degrees
angle B is 47 degrees
y/x = tan 19
y = x (tan 19)
AND...
y/(x - 120) = tan 47
y = (x - 120) (tan 47)
y = (x * tan 47) - (120 * tan 47)
(x * tan 47) - (120 * tan 47) = (x * tan 19)
(x * tan 47) - (x * tan 19) = (120 * tan 47)
x * ((tan 47) - (tan 19)) = (120 * tan 47)
x = (120 * tan 47) / ((tan 47) - (tan 19))
x = (120 * 1.07237) / (1.07237 - 0.34433)
x = 128.68 / 0.72804
x = 176.75 m
y = 176.75 m * tan 19 = 176.75 * 0.34433 = 60.86 m
The building is 60.86 m high