Question: One of the legs of a right triangle measures 13 cm and its hypotenuse measures 18 cm. Find the…

One of the legs of a right triangle measures 13 cm and its hypotenuse measures 18 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.

Solution

To find the measure of the other leg of the right triangle, we can use the Pythagorean theorem. The theorem states: \[ a^2 + b^2 = c^2 \] where \(c\) is the hypotenuse, and \(a\) and \(b\) are the legs of the triangle. Given: \(a = 13 \, \text{cm}\) (one leg), \(c = 18 \, \text{cm}\) (hypotenuse). We need to find \(b\). Substitute the given values into the Pythagorean theorem: \[ 13^2 + b^2 = 18^2 \] Calculate \(13^2\) and \(18^2\): \[ 169 + b^2 = 324 \] Subtract 169 from both sides to solve for \(b^2\): \[ b^2 = 324 - 169 \] \[ b^2 = 155 \] Take the square root of both sides to find \(b\): \[ b = \sqrt{155} \] Calculate \(\sqrt{155}\) and round to the nearest tenth: \[ b \approx 12.5 \] Therefore, the measure of the other leg is approximately \(12.5 \, \text{cm}\).