Question

use the law of sines to find the missing angle of the triangle. find ( mangle b ) to the nearest tenth.

Explanation:

Step1: Apply the Law of Sines

The Law of Sines states that \(\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}\). Here, \(A = 59^{\circ}\), \(a = 50\), \(b = 58\). So, \(\frac{\sin59^{\circ}}{50}=\frac{\sin B}{58}\).

Step2: Solve for \(\sin B\)

Cross - multiply: \(\sin B=\frac{58\times\sin59^{\circ}}{50}\).
We know that \(\sin59^{\circ}\approx0.8572\). Then \(\sin B=\frac{58\times0.8572}{50}=\frac{49.7176}{50}=0.994352\).

Step3: Find the angle \(B\)

\(B=\sin^{- 1}(0.994352)\approx83.9^{\circ}\)

Answer:

\(83.9^{\circ}\)