Question

what is the length of the hypotenuse? if necessary, round to the nearest tenth.

c = \boxed{} inches

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem states that for a right triangle, \( a^2 + b^2 = c^2 \), where \( a \) and \( b \) are the legs, and \( c \) is the hypotenuse. Here, \( a = 27 \) in and \( b = 36 \) in. So we calculate \( 27^2 + 36^2 \).
\( 27^2 = 729 \), \( 36^2 = 1296 \), so \( 729 + 1296 = 2025 \).

Step2: Solve for \( c \)

Now we have \( c^2 = 2025 \), take the square root of both sides: \( c = \sqrt{2025} = 45 \).

Answer:

45