Question

In a right-angled triangle, the length of the hypotenuse is 10 inches and one of the legs is 6 inches. Find the length of the other leg.

Answer 1

To find the length of the other leg in a right-angled triangle, we can use the Pythagorean theorem. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two legs (a and b). The equation can be written as:

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

In this problem:
- \( c = 10 \) inches (the hypotenuse),
- \( a = 6 \) inches (one leg),
- \( b \) is the length of the other leg, which we want to find.

Plugging in the values we have:

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

Calculating the squares:

\[
100 = 36 + b^2
\]

Now, we will isolate \( b^2 \):

\[
b^2 = 100 - 36
\]

\[
b^2 = 64
\]

Now, taking the square root of both sides to find \( b \):

\[
b = \sqrt{64}
\]

\[
b = 8
\]

Thus, the length of the other leg is \( \boxed{8} \) inches.