Question

Find the length of the hypotenuse of a triangle if the lengths of the legs are known.
Step 1: identify the legs and hypotenuse of the right triangle
A = 6
B = 8
C = ?

Step 2: substitute values into the Pythagoreon therom: a² + b² = c²

Answer 1

To find the length of the hypotenuse \( C \) of a right triangle given the lengths of the legs \( A \) and \( B \), we can use the Pythagorean theorem, which states:

\[
a^2 + b^2 = c^2
\]

In this case, we have:

- \( A = 6 \)
- \( B = 8 \)
- \( C = ? \)

Step 1: Identify the legs and hypotenuse of the right triangle.

- Legs: \( A = 6 \) and \( B = 8 \)
- Hypotenuse: \( C \)

Step 2: Substitute values into the Pythagorean theorem:

\[
6^2 + 8^2 = C^2
\]

Calculating the squares:

\[
36 + 64 = C^2
\]

Adding those values together:

\[
100 = C^2
\]

Now, to find \( C \), take the square root of both sides:

\[
C = \sqrt{100}
\]

Calculating the square root:

\[
C = 10
\]

Thus, the length of the hypotenuse \( C \) is \( \boxed{10} \).