Trigonometry · Superchallenge problem

A $10$-metre flagpole stands on top of a $6$-metre building. From a point $P$ on the level ground, the building and the flagpole subtend equal angles (the angle between the lines of sight to the bottom and top of the building equals the angle between the lines of sight to the bottom and top of the pole). How far is $P$ from the base of the building, in metres?