Question

a ski jump ramp has a base of 12 feet, and a height of 5 feet, as shown. how long is the ramp?

Explanation:

Step1: Identify the triangle type

The ramp forms a right - triangle with base \(a = 12\) feet and height \(b = 5\) feet. The ramp length \(x\) is the hypotenuse. We use the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\) (where \(c\) is the hypotenuse, \(a\) and \(b\) are the legs of the right - triangle).

Step2: Substitute values into the formula

Substitute \(a = 12\) and \(b = 5\) into the formula: \(x=\sqrt{12^{2}+5^{2}}\)
First, calculate \(12^{2}=144\) and \(5^{2}=25\). Then \(12^{2}+5^{2}=144 + 25=169\).

Step3: Calculate the square root

Since \(x=\sqrt{169}\), and \(\sqrt{169}=13\) (because \(13\times13 = 169\)).

Answer:

The length of the ramp is 13 feet.