Question

A seven foot ladder, leaning against a wall, touches the wall x feet above the ground. Write an
expression in terms of x for the distance from the foot of the ladder to the base of the wall.

Answer 1

Here we have a the ladder and wall creating a right triangle. The ladder itself being 7 feet is the hypotenuse of the triangle and the distance from the foot of the ladder to the base of the wall is one of the legs. Our equation for right triangles is that the sum of the square of the legs will equal the square of the hypotenuse (Pythagorean theorem) :\[a ^{2} + b ^{2} = c ^{2}\]
Where a and b are legs and c is the hypotenuse. They tell you the other leg is x in length. So all you have to do is substitute 7 for the hypotenuse and x for one of the legs and solve for the other variable. Voila!