Question

if u are using the pythagorean-theorem of a missing leg a=10 c=6 b=?

Answer 1

In order to find the missing leg \( b \) of a right triangle using the Pythagorean theorem, we use the formula:

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

where \( c \) is the hypotenuse, and \( a \) and \( b \) are the two legs of the triangle.

Given:
- \( a = 10 \)
- \( c = 6 \)

However, it appears there is a mistake in the provided values because, in a right triangle, the hypotenuse \( c \) should be the longest side. If \( a = 10 \), then \( c \) cannot be 6.

We will assume you meant that \( c \) is the hypotenuse, but with the current values given, it seems inconsistent because \( a \) cannot be longer than \( c \).

If we instead consider a case where \( c = 10 \) (and thus \( a = 6 \)), we can solve for \( b \) as follows:

1. Rearranging the Pythagorean theorem:

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

2. Substituting the values \( c = 10 \) and \( a = 6 \):

\[
b^2 = 10^2 - 6^2
\]
\[
b^2 = 100 - 36
\]
\[
b^2 = 64
\]
\[
b = \sqrt{64}
\]
\[
b = 8
\]

Thus, if \( c = 10 \) and \( a = 6 \), then \( b \) would equal 8.

If the values were meant to be different, please clarify, and I will assist you accordingly.