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View Full Version : Length between two buildings


gpmn123
Feb 25, 2009, 07:23 PM
The angle of depression of a taller building to the top of a shorter building is 18 degress. The anlge of depression from the top of the taller building to the base of the shorter building is 32 degrees. The height of the shorter building is 200 feet. What is the distance between the two buildings?

Perito
Feb 25, 2009, 08:46 PM
X is the height of the higher tower *above* the 200 ft tower.
D is the distance between towers.

Tan(α) = X/D
Tan(β) = (X+200)/D

Tan(α)/Tan(β) = X/(X+200)
α = 18 degrees
β = 32 degrees.

Calculate the tangents and solve for X