Find the height

Question

At a point on the ground 70 ft from the base of a tree, the distance to the top of the tree is 2 ft more than 3 times the height of the tree. Find the height of the tree.

Answer 1

These words describe a picture, of a right triangle.  Draw it.  One leg will be horizontal, the other will be vertical, and the third side is the hypotenuse.  Label the triangle as follows.

 

Horizontal leg: 70 ft

Vertical leg (tree height) = h

Hypotenuse: 2 + 3h

 

Now use the Pythagorean theorem.