Question

question
one of the legs of a right triangle measures 10 cm and the other leg measures 14 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, \( a = 10 \) cm and \( b = 14 \) cm.

Step2: Substitute values into the formula

Substitute \( a = 10 \) and \( b = 14 \) into the formula: \( c = \sqrt{10^2 + 14^2} \)

Step3: Calculate the squares

\( 10^2 = 100 \) and \( 14^2 = 196 \), so \( c = \sqrt{100 + 196} \)

Step4: Add the values inside the square root

\( 100 + 196 = 296 \), so \( c = \sqrt{296} \)

Step5: Calculate the square root and round

\( \sqrt{296} \approx 17.2 \) (rounded to the nearest tenth)

Answer:

The measure of the hypotenuse is approximately 17.2 cm.