Question

one of the legs of a right triangle measures 9 cm and the other leg measures 1 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 \( b = 1 \) cm.

Step2: Substitute values into the formula

Substitute \( a = 9 \) and \( b = 1 \) into the formula:
\( c = \sqrt{9^2 + 1^2} \)
\( = \sqrt{81 + 1} \)
\( = \sqrt{82} \)

Step3: Calculate the square root and round

\( \sqrt{82} \approx 9.1 \) (rounded to the nearest tenth)

Answer:

The measure of the hypotenuse is approximately \( 9.1 \) cm.