Question

use the law of sines to find the missing angle of the triangle. find m∠b to the nearest tenth. 132.4° 83.9° 37.1° 47.6°

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, $A = 59^{\circ}$, $a = 58$, $b = 50$. So, $\frac{\sin59^{\circ}}{58}=\frac{\sin B}{50}$.

Step2: Solve for $\sin B$

Cross - multiply: $\sin B=\frac{50\times\sin59^{\circ}}{58}$. Calculate $\sin59^{\circ}\approx0.8572$. Then $\sin B=\frac{50\times0.8572}{58}\approx\frac{42.86}{58}\approx0.739$.

Step3: Find the angle $B$

Since $B=\sin^{- 1}(0.739)$. Using a calculator, $B\approx47.6^{\circ}$ (we also check the ambiguous case. But since $a>b$ in a triangle, there is only one non - obtuse solution for $B$ as $A = 59^{\circ}$ and $A + B<180^{\circ}$).

Answer:

$47.6^{\circ}$