Question In Delta ABC a=6 inches, mangle A=121^circ and mangle B=36^circ Find the length of b, to the nearest 10th of an inch. Answer Attemptiout of 2 b=square inches

## Step 1: Finding Angle C<br />### The sum of angles in a triangle is $180^{\circ}$. We have $m\angle A = 121^{\circ}$ and $m\angle B = 36^{\circ}$. Therefore, $m\angle C = 180^{\circ} - 121^{\circ} - 36^{\circ} = 23^{\circ}$.<br /><br />## Step 2: Applying the Law of Sines<br />### The Law of Sines states that $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$. We are given $a=6$ and $m\angle A = 121^{\circ}$, and we need to find $b$. We also know $m\angle B = 36^{\circ}$. So, $\frac{6}{\sin 121^{\circ}} = \frac{b}{\sin 36^{\circ}}$.<br /><br />## Step 3: Solving for b<br />### We can rearrange the equation from Step 2 to solve for $b$: $b = \frac{6 \times \sin 36^{\circ}}{\sin 121^{\circ}}$. Calculating this gives $b \approx \frac{6 \times 0.5878}{0.8572} \approx 4.12$.