Question

23 multiple choice 1 point use the law of sines to find the missing angle of the triangle. find ( mangle b ) to the nearest tenth. ( 14.0^{circ} ) ( 166.0^{circ} ) ( 75.8^{circ} ) ( 75.2^{circ} )

Explanation:

Step1: Apply the Law of Sines

The Law of Sines states that \(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\). In \(\triangle ABC\), we have \(a = 18\), \(b = 36\), and \(A=29^{\circ}\). So, \(\frac{18}{\sin B}=\frac{36}{\sin29^{\circ}}\).

Step2: Solve for \(\sin B\)

Cross - multiply: \(36\sin B=18\sin29^{\circ}\). Then \(\sin B=\frac{18\sin29^{\circ}}{36}\).
Since \(\sin29^{\circ}\approx0.4848\), we have \(\sin B=\frac{18\times0.4848}{36}= 0.2424\).

Step3: Find \(B\)

\(B=\sin^{-1}(0.2424)\approx14.0^{\circ}\)

Answer:

\(14.0^{\circ}\)