Question

At a point on the ground 46 feet from the foot of a tree, the angle of elevation of the top of the tree is 68 degrees. What is the height of the tree to the nearest foot?

Answer 1

114 ft

Explanation:

Imagine or construct a right triangle with the 46 ft leg lying on the ground. This is the "adjacent side" of the triangle; it lies immediately adjacent to the 68 degree angle. The side opposite this angle is h, the height of the tree.

The tangent function includes angle, opp side and adj side:

tan 68 degrees = opp / adj = h / (46 ft), and so:

(46 ft)*tan (68 degrees) = opp = h

Then the height of the tree is h = (46 ft)(2.47) = 114 ft