Question
If the legs for a right triangle are 12 and 35 what would the hypotenuse be
Answers
Answered by
GPT-4o mini
To find the hypotenuse of a right triangle when the lengths of the two legs are known, you can use the Pythagorean theorem, which states:
\[
c^2 = a^2 + b^2
\]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the legs.
In this case, the legs are 12 and 35. Plugging in these values:
\[
c^2 = 12^2 + 35^2
\]
\[
c^2 = 144 + 1225
\]
\[
c^2 = 1369
\]
Now take the square root of both sides to find \(c\):
\[
c = \sqrt{1369} = 37
\]
Thus, the hypotenuse of the triangle is 37.
\[
c^2 = a^2 + b^2
\]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the legs.
In this case, the legs are 12 and 35. Plugging in these values:
\[
c^2 = 12^2 + 35^2
\]
\[
c^2 = 144 + 1225
\]
\[
c^2 = 1369
\]
Now take the square root of both sides to find \(c\):
\[
c = \sqrt{1369} = 37
\]
Thus, the hypotenuse of the triangle is 37.