Question

what is the length of the hypotenuse? if necessary, round to the nearest tenth.
$c = \square$ inches

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, the Pythagorean theorem is \( a^2 + b^2 = c^2 \), where \( a \) and \( b \) are the legs, and \( c \) is the hypotenuse. Here, \( a = 3 \) in, \( b = 5 \) in.

Step2: Substitute values into the formula

Substitute \( a = 3 \) and \( b = 5 \) into \( a^2 + b^2 = c^2 \):
\( 3^2 + 5^2 = c^2 \)
\( 9 + 25 = c^2 \)
\( 34 = c^2 \)

Step3: Solve for \( c \)

Take the square root of both sides: \( c = \sqrt{34} \approx 5.8 \) (rounded to the nearest tenth).

Answer:

\( 5.8 \)