Question
How do I find the length of the hypotenuse of a right-angled triangle with legs of 5 and 12 units?
Answers
GPT-4o mini
To find the length of the hypotenuse of a right-angled triangle with legs of 5 units and 12 units, you can use the Pythagorean theorem. The theorem states that in a right 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 sides (a and b). The formula is:
\[
c^2 = a^2 + b^2
\]
In this case, the lengths of the legs are \(a = 5\) and \(b = 12\). Plugging in these values gives:
\[
c^2 = 5^2 + 12^2
\]
Calculating the squares:
\[
c^2 = 25 + 144
\]
\[
c^2 = 169
\]
Now, to find \(c\), take the square root of both sides:
\[
c = \sqrt{169}
\]
\[
c = 13
\]
Thus, the length of the hypotenuse is **13 units**.
\[
c^2 = a^2 + b^2
\]
In this case, the lengths of the legs are \(a = 5\) and \(b = 12\). Plugging in these values gives:
\[
c^2 = 5^2 + 12^2
\]
Calculating the squares:
\[
c^2 = 25 + 144
\]
\[
c^2 = 169
\]
Now, to find \(c\), take the square root of both sides:
\[
c = \sqrt{169}
\]
\[
c = 13
\]
Thus, the length of the hypotenuse is **13 units**.