Question

bc = round your answer to the nearest hundredth.

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(ABC\) with \(\angle C = 90^{\circ}\), \(\sin A=\frac{BC}{AB}\). Given \(\angle A = 50^{\circ}\) and \(AB = 3\).

Step2: Substitute the values into the formula

We know that \(\sin A=\sin50^{\circ}\approx0.7660\), and from \(\sin A=\frac{BC}{AB}\), we can solve for \(BC\). Rearranging the formula gives \(BC = AB\times\sin A\).
Substitute \(AB = 3\) and \(\sin A=\sin50^{\circ}\) into the formula: \(BC=3\times\sin50^{\circ}\).

Step3: Calculate the value

\(BC = 3\times0.7660=2.298\approx2.30\)

Answer:

\(2.30\)