point A and B are 100m apart and are of the same as the foot of a building. the angle of elevation of the top of the building from point A an B are 21 degrees and 32 degree respectively. how far is A from the building?

Answer 1

make your sketch, and label the top of the building P and the bottom of the building R

In triangle ABP,
angle A = 21°
angle ABP = 148°
so angle APB = 53°

by the sine law:
BP/sin21 = 100/sin53
BP = 100sin21/sin53 = .... you do that, store answer in calculator's memory

in right-angled triangle BPR
cos 32 = BR/BP
BR = BPcos32

so AR = 100 + BR

Answer 2

just realized I made an arithmetic error in finding
angle APB

angle APB = 11° , not 53

so please make the necessary changes.

by the sine law:
BP/sin21 = 100/sin11
BP = 100sin21/sin11 = .... you do that, store answer in calculator's memory

the rest stays the same