Question

alex is building a ramp for a bike competition. he has two rectangular boards. one board is 6 meters long and the other is 5 meters long. if the ramp has to form a right triangle, what should its height be? 3 meters 4 meters 3.3 meters 7.8 meters

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with hypotenuse \(c\) and legs \(a\) and \(b\), \(a^{2}+b^{2}=c^{2}\). Here, assume the two sides of the right - triangle are \(a\) and \(b\), and the hypotenuse \(c\). The hypotenuse is the longest side of a right - triangle. So, if \(c = 6\) (the longer board) and one leg \(b = 5\), we want to find the other leg \(a\).

Step2: Rearrange the Pythagorean theorem

We can rewrite the Pythagorean theorem as \(a=\sqrt{c^{2}-b^{2}}\). Substitute \(c = 6\) and \(b = 5\) into the formula: \(a=\sqrt{6^{2}-5^{2}}=\sqrt{36 - 25}=\sqrt{11}\approx3.3\).

Answer:

3.3 meters