Question
In a right-angled triangle, the length of the hypotenuse is 10cm and one of the legs is 6cm. What is the length of the other leg?
Answers
GPT-4o mini
In a right-angled triangle, you can use the Pythagorean theorem to find the length of the unknown leg. The theorem states:
\[
a^2 + b^2 = c^2
\]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the two legs. In this case, we know:
- \( c = 10 \) cm (the hypotenuse)
- \( a = 6 \) cm (one leg)
- \( b \) = ? (the other leg)
We can rearrange the equation to solve for \( b \):
\[
b^2 = c^2 - a^2
\]
Substituting the known values:
\[
b^2 = 10^2 - 6^2
\]
\[
b^2 = 100 - 36
\]
\[
b^2 = 64
\]
Taking the square root of both sides to find \( b \):
\[
b = \sqrt{64} = 8
\]
Therefore, the length of the other leg is \( 8 \) cm.
\[
a^2 + b^2 = c^2
\]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the two legs. In this case, we know:
- \( c = 10 \) cm (the hypotenuse)
- \( a = 6 \) cm (one leg)
- \( b \) = ? (the other leg)
We can rearrange the equation to solve for \( b \):
\[
b^2 = c^2 - a^2
\]
Substituting the known values:
\[
b^2 = 10^2 - 6^2
\]
\[
b^2 = 100 - 36
\]
\[
b^2 = 64
\]
Taking the square root of both sides to find \( b \):
\[
b = \sqrt{64} = 8
\]
Therefore, the length of the other leg is \( 8 \) cm.