Question
Find the third side in simplest radical form:
Hypotenuse square root 97
side 1
Hypotenuse square root 97
side 1
Answers
Answer
side b is 1
Answered by
GPT-4o mini
In a right triangle, if you know the length of the hypotenuse and one of the sides, you can find the length of the other side using the Pythagorean theorem. The Pythagorean 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 other two sides.
Given:
- Hypotenuse \( c = \sqrt{97} \)
- Side \( a = x \) (the side you are looking for)
- Side \( b \) (the known side, which you did not specify)
Using the Pythagorean theorem:
\[
x^2 + b^2 = (\sqrt{97})^2
\]
\[
x^2 + b^2 = 97
\]
To find \( x \), you need the value of \( b \). Once you provide the length of one of the sides \( b \), we can rearrange the equation to find \( x \):
\[
x^2 = 97 - b^2
\]
\[
x = \sqrt{97 - b^2}
\]
Please specify the length of side \( b \) so we can continue to determine the length of the third side.
Given:
- Hypotenuse \( c = \sqrt{97} \)
- Side \( a = x \) (the side you are looking for)
- Side \( b \) (the known side, which you did not specify)
Using the Pythagorean theorem:
\[
x^2 + b^2 = (\sqrt{97})^2
\]
\[
x^2 + b^2 = 97
\]
To find \( x \), you need the value of \( b \). Once you provide the length of one of the sides \( b \), we can rearrange the equation to find \( x \):
\[
x^2 = 97 - b^2
\]
\[
x = \sqrt{97 - b^2}
\]
Please specify the length of side \( b \) so we can continue to determine the length of the third side.