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

Question

I have no idea where to start for solving this problem. please help

Answer 1

We can solve this by setting up a right triangle with hypotenuse 3h+2 (2 more than 2 times the height of the tree) and legs of h and 70.

 

Next, you'll use the Pythagorean Theorem:

 

h² + 70² = (3h+2)²

h² + 4900 = 9h² + 6h + 6h + 4  (Combine like terms)

h² + 4900 = 9h² + 12h + 4    (Subtract h² from both sides)

4900 = 8h² + 12h + 4 (Subtract 4900 from both sides)

8h² + 12h - 4896 = 0 (Divide entire equation through by 4)

2h² + 3h - 1224 = 0

 

Solve using the quadratic formula:

 

[-b +/- sqrt (b² - 4ac) ] / 2a

 

When you plug and chug through the quadratic formula, you'll get:

h = 24 and h = -25.50

 

The height of the tree can't be a negative value.  Therefore, the height of the tree must be 24 feet.