Question

For Angle Z, create trig ratios for sin, cos, and tan. Imagine a scalene triangle. The left side is labelled 12, the right side is labelled 9, and the bottom side is labelled 15. The top point is labelled Y, the bottom left point is labelled Z, and the point beside it is labelled X.
A. sin(Z) = 9/15, cos(Z)= 12/15, tan(Z) = 9/12
B. sin(Z) = 9/12, cos(Z) = 9/15, tan(Z) = 9/15
C. sin(Z) = 12/15, cos(Z) = 9/15, tan(Z) = 9/15
D. 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 scalene triangle with sides labeled as follows:

- Side opposite angle Z: 9
- Adjacent side to angle Z: 12
- Hypotenuse: 15

We can use the definitions of the trigonometric functions:

1. **Sine (sin)** of angle Z is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse:
\[
\sin(Z) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{9}{15}
\]

2. **Cosine (cos)** of angle Z is defined as the ratio of the length of the adjacent side to the length of the hypotenuse:
\[
\cos(Z) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{12}{15}
\]

3. **Tangent (tan)** of angle Z is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side:
\[
\tan(Z) = \frac{\text{opposite}}{\text{adjacent}} = \frac{9}{12}
\]

Putting it all together, we have:

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

Thus, the correct choice is **A**:
\[
\text{A. } \sin(Z) = \frac{9}{15}, \cos(Z) = \frac{12}{15}, \tan(Z) = \frac{9}{12}
\]