Question

the angle of elevation of the top of a building from a point 80 ft away from the building on level ground is 70° determine the buildings height

Answer 1

Draw a triangle with shortest side on the ground (horiz.). The length of this side is 80 feet. Two angles touch the ground: a right angle, and the 70 degree angle.

Then the height of the building is the 2nd shortest side.

The tangent function is the appropriate one to use here:
opp h
tan 70 deg = -------- = ----------
adj 80 ft
h
Since tan 70 deg = 2.75, 2.75 = -------
80 ft

so h = building height = (80 ft)(2.75) = 219.8 ft