Let h be the height of the tree and d the distance to the top of the tree from the point on the ground. Draw a diagram to visualize the situation:
Since the distance to the top of the tree is 11 ft more than two times the height, then:
Use the Pythagorean Theorem to relate the length of the sides of the right triangle:
Notice that we have obtained a quadratic equation in terms of h. Write it in standard form and use the quadratic formula to solve for h:
Since the height of the tree must be positive, the only solution is h=39ft. To the nearest foot, the height of the tree is 39.
Therefore, the height of the tree is 39 ft.
