Question

what is the approximate value of x? round to the nearest tenth.
3.1 cm
3.9 cm
4.6 cm
5.4 cm

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 50^{\circ}\), the hypotenuse is \(6\) cm, and the side opposite to the \(50^{\circ}\) angle is \(x\).

Step2: Apply the sine formula

We know that \(\sin(50^{\circ})=\frac{x}{6}\).

Step3: Solve for \(x\)

Multiply both sides by \(6\): \(x = 6\times\sin(50^{\circ})\).
Since \(\sin(50^{\circ})\approx0.766\), then \(x=6\times0.766 = 4.596\approx4.6\).

Answer:

\(4.6\) cm (corresponding to the third option)