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.
The angle of elevation from a point 50 feet from the base of the tree to the top of the tree is 30 degrees.
Now tan 30 = height of tree/ distance of the point from the base
=> tan 30 = H / 50
=> 1/ sqrt 3 = H / 50
=> H = 50/sqrt 3
=> 28.86 feet
The height of the tree is 28.86 feet.
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.
We notice that it is formed a right triangle, whose base is of 50 feet long and it's horizontal angle is of 30 degrees.
We notice that the base is the adjacent side from the angle of 30 and the height is the opposite side from the angle.
We'll apply tangent function:
tan 30 = height/50
1/sqrt3 = height/50
height = 50/sqrt3
height = 50*sqrt3/3
The height of the tree is: height = 28.867 feet