calc
posted by michael .
A 18 ft ladder leans against a building so that the angle between the ground and the ladder is 82 ^\circ.
How high does the ladder reach on the building?

I don't understand your notation of 82 ^\circ
but I will assume that the ladder makes an angle of 82° with the ground at the foot of the ladder
sin 82° = height/18
height = 18sin82 = appr 17.8 ft