Question

if c=17 inches and b=15 inches, find the valuse of sin0. write your answer as a fraction. You do not need to simplify

Answer 1

so 8/17?

Answer 2

To find \(\sin(\theta)\) given sides of a triangle, we can use the definition of sine. For a right triangle, if \(c\) is the length of the hypotenuse and \(b\) is one of the legs, then:

\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}.
\]

In this case, we can consider:

- \(c = 17\) inches (the hypotenuse),
- \(b = 15\) inches (the adjacent side).

Since we need the opposite side for sine, we can find it using the Pythagorean theorem:

\[
c^2 = a^2 + b^2,
\]

where \(a\) is the opposite side. Plugging in the values:

\[
17^2 = a^2 + 15^2,
\]
\[
289 = a^2 + 225,
\]
\[
a^2 = 289 - 225,
\]
\[
a^2 = 64,
\]
\[
a = 8 \text{ inches}.
\]

Now that we have the opposite side, we can find \(\sin(\theta)\):

\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{a}{c} = \frac{8}{17}.
\]

So, the value of \(\sin(\theta)\) is \(\frac{8}{17}\).

Answer 3

Yes, that's correct! The value of \(\sin(\theta)\) is \(\frac{8}{17}\) based on the given triangle with \(c = 17\) inches (hypotenuse) and \(b = 15\) inches (one of the legs). So the final answer is:

\[
\sin(\theta) = \frac{8}{17}.
\]