Question

What is the length of the hypotenuse of the triangle?

Triangle A B C. Side A C is 8 centimeters and side C B is 15 centimeters. Hypotenuse A B is unknown.
StartFraction 94 EndFraction cm
StartFraction 161 EndFraction cm
17 cm
23 cm

Answer 1

To find the length of the hypotenuse \( AB \) of triangle \( ABC \), where \( AC \) = 8 cm and \( CB \) = 15 cm, we can apply the Pythagorean theorem, which states:

\[
AB^2 = AC^2 + CB^2
\]

Substituting the given values:

\[
AB^2 = 8^2 + 15^2
\]

Calculating \( 8^2 \) and \( 15^2 \):

\[
8^2 = 64
\]
\[
15^2 = 225
\]

Now add these values:

\[
AB^2 = 64 + 225 = 289
\]

To find \( AB \), we take the square root of 289:

\[
AB = \sqrt{289} = 17 \text{ cm}
\]

Therefore, the length of the hypotenuse \( AB \) is \( \boxed{17} \) cm.