solve the triangle.\nb = (square^{circ}) (do not round until the final answer. then round to the nearest…

Explanation:

Step1: Find angle B

The sum of angles in a triangle is 180°. So $B = 180^{\circ}-A - C$. Given $A = 35^{\circ}$ and $C=76^{\circ}$, then $B=180 - 35-76=69^{\circ}$.

Step2: Use the Law of Sines to find side b

The Law of Sines states that $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$. We know $a = 9$, $A = 35^{\circ}$, and $B=69^{\circ}$. So $b=\frac{a\sin B}{\sin A}=\frac{9\times\sin69^{\circ}}{\sin35^{\circ}}$. Since $\sin69^{\circ}\approx0.9346$ and $\sin35^{\circ}\approx0.5736$, then $b=\frac{9\times0.9346}{0.5736}\approx14.7$.

Step3: Use the Law of Sines to find side c

Using $\frac{a}{\sin A}=\frac{c}{\sin C}$, with $a = 9$, $A = 35^{\circ}$, and $C = 76^{\circ}$. So $c=\frac{a\sin C}{\sin A}=\frac{9\times\sin76^{\circ}}{\sin35^{\circ}}$. Since $\sin76^{\circ}\approx0.9703$ and $\sin35^{\circ}\approx0.5736$, then $c=\frac{9\times0.9703}{0.5736}\approx15.2$.

Answer:

$B = 69^{\circ}$ $b\approx14.7$ $c\approx15.2$