Question

Solution of problem:from the top of a building 55 ft high, the angle of elevation of the top of a vertical pole is 12 degrees, At the bottom of the building, the angle of elevation of the top of the pole is 24 degrees. find the height of the pole.

Answer 1

Hoping you made a diagram,
label the top of the pole P and its bottom Q
label the top of the building A and its bottom B

Now look at triangle PAB.
angle PAB = 90+12 = 102°
angle PBA = 90-24 = 66°
leaving angle APB = 12°

by the sine law:
PB/sin102 = 55/sin12
PB = 55sin102/sin12 , don't work it out yet

in right-angled triangle PQB
sin 24 = PQ/PB
PQ = PB sin24 = 55 sin102 sin24/sin12

now get your calculator out, and do it in one continuous operation.

Answer 2

105.25ft

Answer 3

Good job 👌👍✅🤔🤔