There are two signposts A and B on the edge of the road. A is 400 m to the west of b. A tree is on a bearing of 060 degree from A and a bearing of 330 degree from B Calculate the shortest distance of the tree from the edge of the road.

Answer 1

T is tree location
triangle A T B
angle BAT = 90 - 60 = 30
angle A B T = 90 - 30 = 60 because 360 -330 = 30
ATB is a 30, 60 90 triangle with 90 at T
we want altitude from T to AB
cos 60 = TB/400
TB = 400 cos 60
then
sin 60 = x/TB where x is the altitude we want
x = 400 cos 60 sin 60 = 200 sin 60 = 200 sqrt 3 / 2