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.

3 answers

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.

105.25ft

Good job 👌👍✅🤔🤔