There are two signposts a and b on the edge of the road. A is 400m to the west of B . A tree is on a bearing of 60 degrees from a and on a bearing of 330 degrees from b. Calculate the shortest distance of the tree from the edge of the road
If we label the tree T and the point closest on the road P, then
TP^2 = AP*PB
Knowing the angles involved, we also know that
TP = 2*PB
4(PB)^2 = 4PB*PB
so, since AB = AP+PB, AP=320 and PB=80
So the distance TP = 160