from a window 30ft above the ground, the angle of elevation to the top of the building across the street is 50° and the angle of depression to the base of the building is 20° find the height of the building across the street

Answer 1

I am sure you made a sketch.
On mine, I labeled the window position W, the top of the building across the street T and the bottom of the building B. I also labeled the point where the horizontal from W meets TB as M

In triangle WBM,
tan20° = 30/WM
WM = 30/tan20°

in triangle WMT ,
tan50° = TM/WM
TM = WMtan50 = (30/tan20)(tan50)
= ...

TB = 30 + TM = ...

you do the button-pushing