Question

which triangle below shows the ratio as \\( \sin ( x ) = \frac { a } { c } \\)?

Explanation:

Step1: Recall the sine formula

In a right - triangle, $\sin(x)=\frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Analyze the first triangle

For the first triangle, the side opposite to angle $x$ is $a$, and the hypotenuse is $c$. So, $\sin(x)=\frac{a}{c}$.

Step3: Analyze the second triangle

For the second triangle, the side opposite to angle $x$ is $b$, and the hypotenuse is $c$. So, $\sin(x)=\frac{b}{c}$.

Step4: Analyze the third triangle

For the third triangle, the side opposite to angle $x$ is $c$, and the hypotenuse is $b$. So, $\sin(x)=\frac{c}{b}$.

Answer:

The first triangle.