## Trigonometry (11th Edition) Clone

$b=458$ $c=877$ $B=31^{\circ}30'$
Step 1: Converting the angle to decimal degrees; $58^{\circ}30'=58\frac{30}{60}^{\circ}=58.5^{\circ}$ Step 2: To find $b$, we use the formula $\tan\theta=\frac{a}{b}$. Step 3: $\tan58.5^{\circ}=\frac{748}{b}$ Step 4: $b=\frac{748}{\tan58.5^{\circ}}$ Step 5: Using a calculator, $b\approx458.4$ Step 6: Rounding the answer to three significant figures, $b\approx458$ Step 7: To find $c$, we use the formula $\sin\theta=\frac{a}{c}$. Step 8: $\sin 58.5^{\circ}=\frac{748}{c}$ Step 9: $c=\frac{748}{\sin 58.5^{\circ}}$ Step 10: Using a calculator, $c\approx877.3$ Step 11: Rounding the answer to three significant figures, $c\approx877$ Step 12: As $A+B=90^{\circ}$, $B=90^{\circ}-58^{\circ}30'$ Step 13: Solving, $B=31^{\circ}30'$.