Question

If a leaf on the ground is 80 feet from the base of a tree, and the angle of elevation to the top of the tree from the leaf is 46 degrees. Then how tall is the tree?

Answer 1

57.55 feet

Explanation:

An image was attached to provide the necessary explanations.

Answer 2

82.8424 feet

Explanation:

The leaf, the base of the tree and the top of the tree form a triangle.

The adjacent cathetus to the 46 degrees angle is 80 feet. The opposite cathetus to the 46 degrees angle is the tree height that we want to know. So, using the relation between the opposite cathetus and the adjacent cathetus (so the tangent of the angle), we can find the tree height (h):

tan(46) = h/80 = 1.0355

h = 80*1.0355 = 82.8424 feet