Question

From the top of a building 30 ft tall, the angle of depression to the foot of a building across the street is 60 degrees and the angle of depression to the top of the same building is 70 degrees. How tall is the building?

Answer 1

I am going to assume that you have mistakenly switched your two angles (the angle of depression to the top of the building across the street can not be greater than the angle of depression to that same building)

The distance between the bases of the two buildings is
`tan(90^o-70^o) xx 30 ft`
`= 30tan(20^o)`

(as shown on the diagram).

`x`, the extra height of the first building over the second, is
`=(30 tan(20^o))/(sin(30^o))`

and the height of the second building is
`30( 1 -(tan(20^o))/(sin(30^o))) " feet"`