Question

At a point on the ground 35 ft from base of a tree, the distance to the top of the tree is 1 ft more than 3 times the height of the tree. Find the height of the tree. The height of the tree is ___. (ft^3, ft^2, or ft)(Simply your answer. Round to the nearest foot as needed)

Answer 1

At a point on the ground 35 ft from the base of a tree, the distance to the top of the tree is 1 ft more than 3 times the height of the tree. Find the height of the tree

see the attached figure to better understand the problem

Applying the Pythagorean Theorem

(3h+1)^2=h^2+35^2

9h^2+6h+1=h^2+1,225

solve for h

9h^2-h^2+6h+1-1,225=0

8h^2+6h-1,224=0

Solve the quadratic equation

Using a graphing tool

the solution is

h=12 ft