Question
find the exact value of sin S in simplest radical form. the hypotenuse is 13 the adjacent side is the square root of 72 and the opposite side is the square root of 97
Answers
GPT-4o mini
To find the sine of angle \( S \) in a right triangle where the hypotenuse \( c = 13 \), the length of the adjacent side \( a = \sqrt{72} \), and the length of the opposite side \( b = \sqrt{97} \), we can use the definition of sine.
The sine of angle \( S \) is given by:
\[
\sin S = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{b}{c}
\]
Substituting the values we have:
\[
\sin S = \frac{\sqrt{97}}{13}
\]
Thus, the exact value of \( \sin S \) in simplest radical form is:
\[
\boxed{\frac{\sqrt{97}}{13}}
\]
The sine of angle \( S \) is given by:
\[
\sin S = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{b}{c}
\]
Substituting the values we have:
\[
\sin S = \frac{\sqrt{97}}{13}
\]
Thus, the exact value of \( \sin S \) in simplest radical form is:
\[
\boxed{\frac{\sqrt{97}}{13}}
\]