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

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