The distance of person a to light towet

Question

Person B is standing. 33ft. Farther from tower tan person A. The angle of person A is 42 degrees 10'. Angle B is 47 degrees and 30' what is the distance from person A from tower.

Answer 1

It's assumed that the given angles are measured vertically from the top of the light tower.

The angles of elevation for A and B are therefore 90-42°10'=47°50' and 90-47°30'=42°30'.

The height of the tower can be expressed as xtan47°50' and (x+33)tan42°30', where x is the distance from A to the tower.

So xtan47°50'=(x+33)tan42°30'. So x=33tan42°30'/(tan47°50'-tan42°30')=30.2389/0.1878=161 feet approx.