Question

trig #1
write an equation to find the missing side

cos 37 = \frac{x}{11}

\sin 37 = \frac{x}{37}

\cos 37 = \frac{11}{x}

\sin 37 = \frac{11}{x}

Explanation:

Step1: Recall trigonometric ratios

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\) and \(\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 37^{\circ}\), the adjacent side to \(37^{\circ}\) is \(BC = 11\), and the hypotenuse is \(AB=x\).

Step2: Apply the cosine ratio

Using the formula \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), substituting \(\theta = 37^{\circ}\), adjacent \(=11\) and hypotenuse \(=x\), we get \(\cos37^{\circ}=\frac{11}{x}\).

Answer:

\(\cos37^{\circ}=\frac{11}{x}\) (the third option)