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