Questions: Calculator Mr. Romero attached a ramp to the base of a window sill so that the family cat could more easily climb onto it. The ramp is 84 inches long. The window sill is 50 inches above the floor. What is the distance from the base of the ramp to the base of the wall? Enter your answer, rounded to the nearest tenth, in the box. 67.5 in.

Solution Steps

To find the distance from the base of the ramp to the base of the wall, we can use the Pythagorean theorem. The ramp forms the hypotenuse of a right triangle, with the height of the window sill as one leg and the distance from the base of the ramp to the base of the wall as the other leg. We can solve for the unknown leg using the formula \(a^2 + b^2 = c^2\).

We are given a right triangle where the ramp forms the hypotenuse (\(c\)) and the height of the window sill forms one leg (\(a\)). We need to find the length of the other leg (\(b\)).

The Pythagorean theorem states that for a right triangle: \[ a^2 + b^2 = c^2 \] Given: \[ c = 84 \] \[ a = 50 \]

Rearrange the Pythagorean theorem to solve for \(b\): \[ b^2 = c^2 - a^2 \] \[ b = \sqrt{c^2 - a^2} \]

Substitute the given values: \[ b = \sqrt{84^2 - 50^2} \] \[ b = \sqrt{7056 - 2500} \] \[ b = \sqrt{4556} \] \[ b \approx 67.5 \]

Final Answer