Question

your mathematics teacher tells you that a right triangle has a hypotenuse of 13 and a leg of 5. she asks you to find the other leg of the triangle. what is your answer?

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse, and \(a\), \(b\) are the legs. Let the known leg be \(a = 5\), hypotenuse \(c=13\), and the unknown leg be \(b\).

Step2: Rearrange the formula to solve for \(b\)

We can rewrite the Pythagorean theorem as \(b^{2}=c^{2}-a^{2}\). Substitute \(a = 5\) and \(c = 13\) into the formula: \(b^{2}=13^{2}-5^{2}\). Calculate \(13^{2}=169\) and \(5^{2}=25\), so \(b^{2}=169 - 25=144\).

Step3: Find the value of \(b\)

Take the square root of both sides: \(b=\sqrt{144}=12\) (we take the positive root since length cannot be negative).

Answer:

12