Answer to Question #254886 in Algebra for Kat

Question

I if a 12 foot ladder is leaned against the top of 10 foot high wall, how far will the base of the ladder be from the bottom of the wall? Round your answer to the nearest tenth of a foot.

Answer 1

The ladder is the hypotenuse of a right angled triangle. The height is 10 feet. The base of the triangle is what we want. By the Pythagoras theorem:

$10^{2}+ b^{2}=12^{2}$

$b^{2}=12^{2}-10^{2}$

$b^{2}=44$

$b=\sqrt{44}$

$b=6.63$ feet

Rounding off to the nearest tenth of a foot; b= 6.6 feet.

The base of the ladder will be 6.6 feet from the bottom of the wall