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how do you do this angle of depression problem?
From the top of a building a woman observes a car moving toward her on a level road. The angle of depression of the car changes from 28 degrees to 43 degrees during the period of observation. If the car travels 230 ft during this time. Hot tall is the building?
When the angle of depression (angle from the horizontal at the top of the building to the car) was at 28 degrees:
Tan(28) = H/D
H = D Tan(28)
where: H = height of building; D = distance of the car from base of bldg
When angle of depression is at 43 degrees and car moved 230 feet:
Tan(43) = H/(D - 230)
H = (D - 230)Tan(43)
Equating both equations (eliminating H)
(D - 230)Tan(43) = D Tan(28)
D Tan(43) - D Tan(28) = 230 Tan(43)
D = 230 Tan(43)/(Tan(43) - Tan(28)
Substituting D back into H = D Tan(28)
H = 230 Tan(43) Tan(28)/((Tan(43) - Tan(28))
H = 114.04/(0.9325 - 0.5317)
H = 284.53 feet <--- Height of building