Question

What is the length of the missing leg? If necessary, round to the nearest ten
b =
inches

a = 10, c = 6

Answer 1

To find the length of the missing leg \( b \) in a right triangle, we can use the Pythagorean theorem, which states:

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

where:
- \( a \) is one leg,
- \( b \) is the missing leg,
- \( c \) is the hypotenuse.

Given:
- \( a = 10 \) inches,
- \( c = 6 \) inches.

However, it seems there might be an error in your provided values because the hypotenuse \( c \) should be the longest side of a right triangle. In any right triangle, \( c \) should be greater than \( a \).

If you meant \( c \) as a hypotenuse (which typically should be longer than the legs), then the given values do not create a valid right triangle.

If instead, the values are \( a = 6 \) inches (the shorter leg) and \( c = 10 \) inches (the hypotenuse), we can find \( b \) using the corrected values:

1. Substitute the values into the Pythagorean theorem:

\[
6^2 + b^2 = 10^2
\]

2. Calculate the squares:

\[
36 + b^2 = 100
\]

3. Solve for \( b^2 \):

\[
b^2 = 100 - 36
\]
\[
b^2 = 64
\]

4. Take the square root of both sides:

\[
b = \sqrt{64} = 8 \text{ inches}
\]

Thus, if we adjust for the correct positioning of \( a \) and \( c \), the length of the missing leg \( b \) would be **8 inches**. If you need it rounded to the nearest ten, it would be **10 inches**.

Please verify the values for clarity.