Question

which equation could be used to find the value of x?

cos 49° = \frac{x}{55}

tan 49° = \frac{x}{55}

cos 49° = \frac{55}{x}

tan 49° = \frac{55}{x}

Explanation:

Step1: Recall the trigonometric ratio definitions

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\), \(\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}\), \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\).
For the given right - triangle with angle \(49^{\circ}\), the side opposite to the \(49^{\circ}\) angle is \(x\), and the side adjacent to the \(49^{\circ}\) angle is \(55\).

Step2: Apply the tangent ratio

Since \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\), when \(\theta = 49^{\circ}\), \(\text{opposite}=x\) and \(\text{adjacent} = 55\), we have \(\tan49^{\circ}=\frac{x}{55}\).

Answer:

\(\tan49^{\circ}=\frac{x}{55}\) (the second option)