You have a 12 foot ladder and need to reach exactly 9 feet up the wall. How far away from the wall should you place the ladder so that you can reach your desired location?

Pythagorean thoerem

we imagine the wall as a leg of a right triangle, the ladder is the hypotonuse and the distance from the bottom of the ladder to the wall is the other leg

so if we have a right triangle with leg length a and b and hypotnuse length c then

a²+b²=c²

so

given that one of the legs is 9ft (9 ft is the height of the triangle)

and the hypotnuse is 12 ft (length of ladder)

then say the last leg is x

so

x²+9²=12²

x²+81=144

mius 81 both sides

x²=63

sqrt both sides

x=√63

x=3√7

you should place it 3√7ft or about 7.9 or 8ft away