A20 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?

Hey!

The top of the ladder reaches approximately 16 feet up the tree.

Hope this helps!

You will see that the ladder, tree and ground form a right-angled triangle and so we can use Pythagoras' Theorem: c^2 = a^2 + b^2, where c is the hypotenuse (in this case the length of the ladder) and a and b are side lengths (in this case the distance between the tree and the ladder and the height that the ladder goes up the tree)

c^2 = a^2 + b^2
20^2 = 12^2 + b^2
400 = 144 + b^2
b^2 = 256
b = 16 feet