A 15 m flagpole stands on level ground. from point P, due west of the flagpole the angle of elevation of the top of the pole is 38 degrees. From point Q, due north of the flagpole, the flagpole has an angle of elevation of 25 degrees. Find the distance of PQ, correct to one decimal place.

Answer 1

Label the top of the pole as T and its base as O
in triangle OTP,
tan38 = 15/OP
OP = 15/tan 38

in triangle TOP,
cos 25 + 15/OQ
OQ = 15/tan25

in the right-angled triangle POQ
PQ^2 = OP^2 + OQ^2

I will let you finish it.