Question

Find the exact value of sin Z in simplest radical form. the hypotenuse is 15 and the adjacent side is 9 and the opposite side is 12

Answer 1

To find the value of \( \sin Z \) in a right triangle, we use the definition of the sine function:

\[
\sin Z = \frac{\text{opposite side}}{\text{hypotenuse}}
\]

In this case, you provided that the hypotenuse is 15 and the opposite side is 12.

Now we can substitute these values into the sine formula:

\[
\sin Z = \frac{12}{15}
\]

Next, we simplify the fraction:

\[
\sin Z = \frac{12 \div 3}{15 \div 3} = \frac{4}{5}
\]

Thus, the exact value of \( \sin Z \) in simplest radical form is:

\[
\boxed{\frac{4}{5}}
\]