Question 850113
The ladder, the ground, and the wall of the house form a right triangle.
One leg is the 20-foot wall height from the ground to the spotlight location.
The other leg is the distance from the foot of the ladder to the house.
If the lengths of those legs, in feet, are 20 and 15, the length, in feet, of the hypotenuse is
{{{sqrt(20^2+15^2)=sqrt(625)=25}}} .
That is based on the Pythagorean theorem, that says that
{{{hypotenuse^2=leg[1]^2+leg[2]^2}}} .
So the ladder must be at least {{{highlight(25feet)}}} long.