Question

one of the legs of a right triangle measures 9 cm and the other leg measures 8 cm. find the measure of the hypotenuse. if necessary, round to the nearest tenth.

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, the Pythagorean theorem states that \( c = \sqrt{a^2 + b^2} \), where \( a \) and \( b \) are the legs, and \( c \) is the hypotenuse. Here, \( a = 9 \) cm and \( b = 8 \) cm.

Step2: Substitute values into the formula

First, calculate \( a^2 \) and \( b^2 \): \( a^2 = 9^2 = 81 \), \( b^2 = 8^2 = 64 \). Then, add them: \( 81 + 64 = 145 \). Now, take the square root: \( c = \sqrt{145} \approx 12.0 \) (rounded to the nearest tenth).

Answer:

The measure of the hypotenuse is approximately \( 12.0 \) cm.