Question

5 mi.
8 mi.
what is the length of the hypotenuse? if necessary, round to the nearest tenth.
c = miles
submit

Explanation:

Step1: Identify the formula

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, \( a = 8 \) mi, \( b = 5 \) mi.

Step2: Substitute values

Substitute \( a = 8 \) and \( b = 5 \) into the formula: \( 8^2 + 5^2 = c^2 \). Calculate \( 8^2 = 64 \) and \( 5^2 = 25 \), so \( 64 + 25 = c^2 \), which simplifies to \( 89 = c^2 \).

Step3: Solve for c

Take the square root of both sides: \( c = \sqrt{89} \). Calculate \( \sqrt{89} \approx 9.43398 \), and round to the nearest tenth: \( c \approx 9.4 \).

Answer:

\( 9.4 \)