Question
In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. What is the length of the remaining side?
Answers
GPT-4o mini
In a right-angled triangle, we can use the Pythagorean theorem to find the length of the remaining side. The Pythagorean theorem states that:
\[
c^2 = a^2 + b^2
\]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the other two sides.
In this case, we know that the hypotenuse \( c = 10 \) cm, and one of the other sides \( a = 6 \) cm. We need to find the length of the remaining side \( b \).
Substituting the known values into the Pythagorean theorem gives:
\[
10^2 = 6^2 + b^2
\]
Calculating the squares:
\[
100 = 36 + b^2
\]
To find \( b^2 \), we can rearrange the equation:
\[
b^2 = 100 - 36
\]
\[
b^2 = 64
\]
Now, taking the square root of both sides to find \( b \):
\[
b = \sqrt{64} = 8
\]
Thus, the length of the remaining side is:
\[
\boxed{8 \text{ cm}}
\]
\[
c^2 = a^2 + b^2
\]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the other two sides.
In this case, we know that the hypotenuse \( c = 10 \) cm, and one of the other sides \( a = 6 \) cm. We need to find the length of the remaining side \( b \).
Substituting the known values into the Pythagorean theorem gives:
\[
10^2 = 6^2 + b^2
\]
Calculating the squares:
\[
100 = 36 + b^2
\]
To find \( b^2 \), we can rearrange the equation:
\[
b^2 = 100 - 36
\]
\[
b^2 = 64
\]
Now, taking the square root of both sides to find \( b \):
\[
b = \sqrt{64} = 8
\]
Thus, the length of the remaining side is:
\[
\boxed{8 \text{ cm}}
\]