Question

1. ms. green 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: Solve for \(b\)

Rearrange the formula to solve for \(b\): \(b^2 = c^2 - a^2\). Substitute \(c = 13\) and \(a = 5\) into the formula: \(b^2 = 13^2 - 5^2 = 169 - 25 = 144\). Then take the square root of both sides: \(b=\sqrt{144}=12\).

Answer:

The length of the other leg is 12.