Question

a ramp is built outside a hospital at a height of 8 feet and reaches 15 feet from the building. how long is the ramp?

Explanation:

Step1: Identify the problem as a right - triangle problem

The ramp forms a right - triangle with the ground and the height of the hospital. The horizontal distance from the building is one leg ($a = 15$ feet) and the height of the hospital is the other leg ($b = 8$ feet). We want to find the length of the hypotenuse $c$ (the length of the ramp).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is $c^{2}=a^{2}+b^{2}$. Substitute $a = 15$ and $b = 8$ into the formula: $c^{2}=15^{2}+8^{2}=225 + 64=289$.

Step3: Solve for $c$

Take the square root of both sides. Since $c>0$, $c=\sqrt{289}=17$ feet.

Answer:

17 feet