Question
In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the legs is 6 cm. 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 other leg. The theorem states that:
\[
a^2 + b^2 = c^2
\]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the legs.
Given:
- \(c = 10 \, \text{cm}\) (the hypotenuse)
- \(a = 6 \, \text{cm}\) (one of the legs)
- \(b\) is the length of the other leg we need to find.
Substituting the known values into the Pythagorean theorem:
\[
6^2 + b^2 = 10^2
\]
Calculating the squares:
\[
36 + b^2 = 100
\]
Now, isolate \(b^2\):
\[
b^2 = 100 - 36
\]
\[
b^2 = 64
\]
Taking the square root of both sides gives:
\[
b = \sqrt{64}
\]
\[
b = 8
\]
Thus, the length of the other leg is \(8 \, \text{cm}\).
\[
a^2 + b^2 = c^2
\]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the legs.
Given:
- \(c = 10 \, \text{cm}\) (the hypotenuse)
- \(a = 6 \, \text{cm}\) (one of the legs)
- \(b\) is the length of the other leg we need to find.
Substituting the known values into the Pythagorean theorem:
\[
6^2 + b^2 = 10^2
\]
Calculating the squares:
\[
36 + b^2 = 100
\]
Now, isolate \(b^2\):
\[
b^2 = 100 - 36
\]
\[
b^2 = 64
\]
Taking the square root of both sides gives:
\[
b = \sqrt{64}
\]
\[
b = 8
\]
Thus, the length of the other leg is \(8 \, \text{cm}\).