Question

unit test
google classroom
microsoft teams
you might need: calculator
∠b =
round your answer to the nearest hundredth.

Explanation:

Step1: Identify trigonometric ratio

In right - triangle \(ABC\) with right - angle at \(C\), we know the opposite side to \(\angle B\) is \(AC = 3\) and the hypotenuse \(AB = 7\). We use the sine function since \(\sin B=\frac{\text{opposite}}{\text{hypotenuse}}\). So \(\sin B=\frac{AC}{AB}\).

Step2: Substitute values

Substitute \(AC = 3\) and \(AB = 7\) into the sine formula: \(\sin B=\frac{3}{7}\).

Step3: Find the angle

To find \(\angle B\), we take the inverse - sine of \(\frac{3}{7}\), i.e., \(B=\sin^{- 1}(\frac{3}{7})\). Using a calculator, \(B=\sin^{-1}(\frac{3}{7})\approx25.38^{\circ}\).

Answer:

\(25.38\)