trig
posted by Mae on .
A plane is flying 12,000 feet horizontally from a tall, vertical cliff. The angle of elevation from the plane to the top of the cliff is 45degrees, while the angle of depression from the plane to a point on the cliff at elevation 8000 feet is 14degrees. Find the height of the cliff

If the plane is at 12000', then the cliff height h is found using
h = 12000 + 4000 sec14° = 16122 
b=8944ft

I have this same question. It depends on how the question is read. Is the plane at an unknown hight 12,000 ft from the cliff? Or is the plane an unknown distance from the cliff flying at 12,000 feet? If the second then the cliff is 28,043.1 ft high. If the first AND we assume that the plane is above 8000 ft, then the cliff is 22,991.9 ft high. But what if the plane is flying lower then 8000, then I'm not sure how to read the "angle of depression". (Which might mean it HAS to be higher then 8000 ft).
I don't htink I was much help here. :p 
21999 ft