Question
Find the third side in simplest radical form
hypotenuse 5
side 4
hypotenuse 5
side 4
Answers
Answer
Now for square root 97 and 1
Answered by
GPT-4o mini
To find the third side of a right triangle when the hypotenuse and one side 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 other two sides.
In this case, let \(c = 5\) (the hypotenuse) and \(a = 4\) (one of the sides). We need to find \(b\) (the other side). The equation becomes:
\[
5^2 = 4^2 + b^2
\]
Calculating the squares:
\[
25 = 16 + b^2
\]
Now, subtract 16 from both sides:
\[
25 - 16 = b^2
\]
\[
9 = b^2
\]
To find \(b\), take the square root of both sides:
\[
b = \sqrt{9} = 3
\]
Thus, the length of the third side is:
\[
\boxed{3}
\]
\[
c^2 = a^2 + b^2
\]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the other two sides.
In this case, let \(c = 5\) (the hypotenuse) and \(a = 4\) (one of the sides). We need to find \(b\) (the other side). The equation becomes:
\[
5^2 = 4^2 + b^2
\]
Calculating the squares:
\[
25 = 16 + b^2
\]
Now, subtract 16 from both sides:
\[
25 - 16 = b^2
\]
\[
9 = b^2
\]
To find \(b\), take the square root of both sides:
\[
b = \sqrt{9} = 3
\]
Thus, the length of the third side is:
\[
\boxed{3}
\]