Question

one of the legs of a right triangle measures 6 cm and the other leg measures 15 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 is \( c = \sqrt{a^2 + b^2} \), where \( a \) and \( b \) are the legs, and \( c \) is the hypotenuse. Here, \( a = 6 \) cm and \( b = 15 \) cm.

Step2: Substitute values into the formula

First, calculate \( a^2 \) and \( b^2 \): \( a^2 = 6^2 = 36 \), \( b^2 = 15^2 = 225 \). Then, add them: \( 36 + 225 = 261 \).

Step3: Take the square root

Now, find \( c = \sqrt{261} \approx 16.2 \) (rounded to the nearest tenth).

Answer:

The measure of the hypotenuse is approximately \( 16.2 \) cm.