solving a triangle given sas information
using the law of cosines, a =
rounded to the nearest tenth.
complete
use your answer above to find m∠b. to the
nearest degree, m∠b =
complete
using the sum of the angle measures of a triangle,
m∠c =
done

Question

Accepted Answer

# Explanation:
## Step1: Use the Law of Cosines to find $a$
The Law of Cosines formula is $a^{2}=b^{2}+c^{2}-2bc\cos A$. Here, $b = 3.7$, $c = 4.0$, and $A=33^{\circ}$.
$$
\begin{align*}
a^{2}&=3.7^{2}+4.0^{2}-2\times3.7\times4.0\times\cos(33^{\circ})\
a^{2}&=13.69 + 16-29.6\times0.8387\
a^{2}&=29.69-24.8255\
a^{2}&=4.8645\
a&\approx2.2
\end{align*}
$$
## Step2: Use the Law of Sines to find $m\angle B$
The Law of Sines formula is $\frac{\sin B}{b}=\frac{\sin A}{a}$. Substitute $a = 2.2$, $b = 3.7$, and $A = 33^{\circ}$
$$
\begin{align*}
\sin B&=\frac{b\sin A}{a}\
\sin B&=\frac{3.7\times\sin(33^{\circ})}{2.2}\
\sin B&=\frac{3.7\times0.5446}{2.2}\
\sin B&=\frac{2.015}{2.2}\
\sin B&\approx0.9159\
B&\approx66^{\circ}
\end{align*}
$$
## Step3: Use the angle - sum property of a triangle to find $m\angle C$
The sum of angles in a triangle is $180^{\circ}$. So $m\angle C=180-(m\angle A + m\angle B)$
$$
\begin{align*}
m\angle C&=180-(33 + 66)\
m\angle C&=81^{\circ}
\end{align*}
$$

# Answer:
$m\angle B = 66^{\circ}$, $m\angle C=81^{\circ}$

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QUESTION IMAGE

Question

Explanation:

Step1: Use the Law of Cosines to find \(a\)

Step2: Use the Law of Sines to find \(m\angle B\)

Step3: Use the angle - sum property of a triangle to find \(m\angle C\)

Answer: