Question

use the law of sines to find the missing angle of the triangle. find ( mangle b ) to the nearest tenth. ( 60.6^{circ} ) ( 141.2^{circ} ) ( 69.4^{circ} ) ( 38.8^{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 this triangle, let \(a = 18\), \(A=\angle B\), \(b = 22\), and \(B = 50^{\circ}\). So, \(\frac{18}{\sin B}=\frac{22}{\sin50^{\circ}}\).

Step2: Solve for \(\sin B\)

Cross - multiply: \(18\times\sin50^{\circ}=22\times\sin B\). Then \(\sin B=\frac{18\times\sin50^{\circ}}{22}\).
We know that \(\sin50^{\circ}\approx0.7660\), so \(\sin B=\frac{18\times0.7660}{22}=\frac{13.788}{22}\approx0.6267\).

Step3: Find \(B\)

Take the inverse sine: \(B=\sin^{- 1}(0.6267)\approx38.8^{\circ}\).

Answer:

\(38.8^{\circ}\)