Question

A 20-foot ladder is leaning against a tree. The bottom of the ladder is 12 feet away from the bottom of the tree. Approximately how high up the tree does the top of the ladder reach?

Answer 1

We want to use the Pythagorean theorem to find the missing length of the right triangle described in the word problem.

The Pythagorean Theorem is a^2 + b^2 = c^2, where a and b are the side lengths of the right triangle, and c is the hypotenuse.
If we know the lengths of two sides of a triangle, we can always find the length of the third side using this formula.

We're given the lengths of one of the sides (12) and the hypotenuse (20). We plug these numbers into our equation and then solve for x.
(x represents the how high the ladder reaches)

x^2 + 12^2 = 20^2
x^2 + 144 = 400
x^2 + 144 - 144 + 400 - 144
x^2 = 256

Now, find the square root of each side of the parenthesis.

√x^2 = √256
x = 16.

The answer is 16.

If there's anything you don't understand, I would highly recommend going to the website Khan Academy and watch his videos regarding it, he explains things much better than I ever could.

Hope this helps!!

Answer 2

Draw out and you'll see if make a triangle.  Use Pythagorean theorem

you are given c and the other side
So,
c2 = a2 + b2
20^2 = 12^2 + b2
400 = 144 +b2
256 = b2
b = 16

Hope this helps