Question

which trig functions are you going to use based on how you labled the triangle with 14 being the opposite side and x being the hypotenuse side with 36 degrees on the adjacent side

Answer 1

In the triangle you described, with 14 as the opposite side, \(x\) as the hypotenuse, and the angle of 36 degrees adjacent to the side measuring 14, you would use the sine and cosine functions to find the relationships between the sides of the triangle.

1. **Sine Function**: Since you have the opposite side and the hypotenuse, you can use the sine function:
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]
Therefore:
\[
\sin(36^\circ) = \frac{14}{x}
\]

2. **Cosine Function**: If you wanted to find the adjacent side, you could use the cosine function:
\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}
\]

However, in this case, you would need to find or label the adjacent side first to use it effectively.

Thus, you would primarily use the sine function to find \(x\), the hypotenuse.