Question

which shows the correct trig equation?
\\( \sin \theta = 14 / 5 \\)
\\( \cos \theta = 5 / 14 \\)
\\( \tan \theta = 14 / 5 \\)
\\( \sin \theta = 5 / 14 \\)

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 the given right - triangle, the side opposite to \(\theta\) is \(5\), and the hypotenuse is \(14\).

Step2: Calculate \(\sin\theta\)

Using the formula \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), we substitute the values: \(\sin\theta=\frac{5}{14}\)

Answer:

\(\sin\theta = 5/14\) (the red option)