Question

use the law of sines to solve for b. finally, use a calculator to evaluate b.
round your answer to the nearest hundredth.

Explanation:

Step1: Recall Law of Sines formula

The Law of Sines states $\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$. Here, we have $\frac{\sin(62^\circ)}{6}=\frac{\sin(69^\circ)}{b}$, so we solve for $b$ as $b = \frac{6\sin(69^\circ)}{\sin(62^\circ)}$.

Step2: Calculate sine values

First, find $\sin(69^\circ)\approx0.9336$ and $\sin(62^\circ)\approx0.8829$.

Step3: Substitute and compute $b$

Substitute these values into the formula: $b=\frac{6\times0.9336}{0.8829}=\frac{5.6016}{0.8829}\approx6.34$.

Answer:

$6.34$