Question

For angle Z create trig ratios for sin, cos, and tan.
Point Y is 90 degrees and the opposite side is 15. The opposite of angle X is 12 and the opposite of angle Z is 9


Sin(z)=9/15, cos(z)=12/15, tan(z)=9/12
Sin(z)=9/12, cos(z)=9/15, tan(z)9/15
Sin(z)=12/15,cos(z)=9/15, tan(z)=9/15
Sin(z)=9/12, cos(z)=9/15, tan(z)=9/15

Answer 1

To find the trigonometric ratios for angle \( Z \) in the given triangle, we need to define the sides in relation to angle \( Z \):

1. **Opposite side to angle \( Z \)**: \( 9 \)
2. **Adjacent side to angle \( Z \)**: \( 12 \)
3. **Hypotenuse** (which can be calculated using the Pythagorean theorem):

\[
\text{Hypotenuse} = \sqrt{(\text{opposite})^2 + (\text{adjacent})^2} = \sqrt{9^2 + 12^2} = \sqrt{81 + 144} = \sqrt{225} = 15
\]

Now we can determine the trigonometric ratios:

- **\(\sin(Z)\)** (opposite/hypotenuse):

\[
\sin(Z) = \frac{\text{opposite to } Z}{\text{hypotenuse}} = \frac{9}{15}
\]

- **\(\cos(Z)\)** (adjacent/hypotenuse):

\[
\cos(Z) = \frac{\text{adjacent to } Z}{\text{hypotenuse}} = \frac{12}{15}
\]

- **\(\tan(Z)\)** (opposite/adjacent):

\[
\tan(Z) = \frac{\text{opposite to } Z}{\text{adjacent to } Z} = \frac{9}{12}
\]

Putting these ratios together, we have:

- \(\sin(Z) = \frac{9}{15}\)
- \(\cos(Z) = \frac{12}{15}\)
- \(\tan(Z) = \frac{9}{12}\)

From your options, the correct answer is:

\[
\sin(Z) = \frac{9}{15}, \quad \cos(Z) = \frac{12}{15}, \quad \tan(Z) = \frac{9}{12}
\]

So the right choice is:

**Sin(Z) = 9/15, cos(Z) = 12/15, tan(Z) = 9/12**.