Question

14/20 which triangle below shows the ratio as $\sin(x)=\frac{b}{c}$?

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

Step3: Analyze the second triangle

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

Step4: Analyze the third triangle

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

Step5: Analyze the fourth triangle

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

Answer:

The fourth triangle.