The angle of elevation of the top of a tree from a point 50 feet from it's base is 30 degrees . What is the height of the tree.

Let  B be the base of the tree, T the top of the tree. Let
P be the point 50 ft from the base B.

So BP = 50
ft.

BT = height of the tree to be
determined.

Angle BPT = 30
deg.

Angle PBT = 90
degree.

Therefore  in the right angled triangle, BT/BP =
tan30.

Therefore BT = BP*tan30
deg

BT = 50* (1/sqrt3) ft.= 28.87 ft
nearly.

Therefore the height of the tree is 28.87
ft.