Question

trig #1
write an equation to find the missing side
cos 32 = \frac{x}{13}
sine 32 = \frac{x}{13}
tan 32 = \frac{13}{x}
tan 32 = \frac{x}{13}

Explanation:

Step1: Recall trigonometric ratios

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\), \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). For angle \(A = 32^{\circ}\), the opposite side to angle \(A\) is \(BC=x\) and the adjacent side to angle \(A\) is \(AC = 13\).

Step2: Apply the tangent ratio

Using the formula \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\), when \(\theta = 32^{\circ}\), \(\text{opposite}=x\) and \(\text{adjacent}=13\). So, \(\tan32^{\circ}=\frac{x}{13}\)

Answer:

\(\tan32=\frac{x}{13}\) (the fourth option)