Question

which shows the correct trig equation?
\\( \sin 20 = 5 / 12 \\)
\\( \cos 20 = 5 / 12 \\)
\\( \tan 12 = 20 / 5 \\)
\\( \sin 5 = 20 / 12 \\)

Explanation:

Step1: Recall trigonometric ratios

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\).
For \(\theta = 20^{\circ}\), the opposite side is \(5\) and the hypotenuse is \(12\).

Step2: Apply the sine formula

Using \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), when \(\theta = 20^{\circ}\), we have \(\sin20^{\circ}=\frac{5}{12}\).

Answer:

\(\sin 20 = 5/12\) (the orange option)