Question
In the right triangle shown, the length of AC = 5 and the length of BC = 6. What is the length of AB?
Answers
GPT-4o mini
In the right triangle, we can use the Pythagorean theorem to find the length of \( AB \). The Pythagorean theorem states that:
\[
AB^2 = AC^2 + BC^2
\]
where \( AB \) is the hypotenuse, and \( AC \) and \( BC \) are the other two sides. Given:
- \( AC = 5 \)
- \( BC = 6 \)
We can substitute these values into the theorem:
\[
AB^2 = 5^2 + 6^2
\]
Calculating the squares:
\[
AB^2 = 25 + 36
\]
\[
AB^2 = 61
\]
To find \( AB \), we take the square root of both sides:
\[
AB = \sqrt{61}
\]
Thus, the length of \( AB \) is:
\[
\boxed{\sqrt{61}}
\]
\[
AB^2 = AC^2 + BC^2
\]
where \( AB \) is the hypotenuse, and \( AC \) and \( BC \) are the other two sides. Given:
- \( AC = 5 \)
- \( BC = 6 \)
We can substitute these values into the theorem:
\[
AB^2 = 5^2 + 6^2
\]
Calculating the squares:
\[
AB^2 = 25 + 36
\]
\[
AB^2 = 61
\]
To find \( AB \), we take the square root of both sides:
\[
AB = \sqrt{61}
\]
Thus, the length of \( AB \) is:
\[
\boxed{\sqrt{61}}
\]