to calculate the height of the tower david measured the angle of elevation of the top of the tower from point A to B 42degrees. He moved then 30meter closer to the tower and from the point B the angle of elevation to the top of the tower to be 50degree. Determine the height of the tower

Answer 1

Did you make a sketch?

I labeled the tower as PQ, with Q and the extended line of AB
In triangle PAB
angle A = 42°, angle ABP = 130°
then angle APB = 8°
by sine law:
BP/sin42 = 30/sin8
BP = 30sin42/sin8

In the right-angled triangle BPQ
sin50 = PQ/BP
PQ = BPsin50
= (30sin42/sin8)(sin50)

carry on with the button-pushing