solve the triangle shown to the right.
round the lengths of sides to the nearest
tenth and angles to the nearest degree.
c≈
(do not round until the final answer. then round to the nearest tenth as needed.)
a≈°
(round to the nearest degree as needed.)
b≈°
(round to the nearest degree as needed.)

Question

Accepted Answer

# Explanation:
## Step1: Use the Law of Cosines to find side $c$
The Law of Cosines formula is $c^{2}=a^{2}+b^{2}-2ab\cos C$.
Given $a = 7$, $b = 5$, and $C=98^{\circ}$, we substitute these values into the formula:
$$
\begin{align*}
c^{2}&=7^{2}+5^{2}-2\times7\times5\times\cos(98^{\circ})\
c^{2}&=49 + 25-70\times(-0.139173)\
c^{2}&=74+9.74211\
c^{2}&=83.74211\
c&=\sqrt{83.74211}\approx9.1
\end{align*}
$$
## Step2: Use the Law of Sines to find angle $A$
The Law of Sines formula is $\frac{\sin A}{a}=\frac{\sin C}{c}$.
Substituting $a = 7$, $c\approx9.1$, and $C = 98^{\circ}$ into the formula:
$$
\begin{align*}
\sin A&=\frac{a\sin C}{c}\
\sin A&=\frac{7\times\sin(98^{\circ})}{9.1}\
\sin A&=\frac{7\times0.990268}{9.1}\
\sin A&=\frac{6.931876}{9.1}\approx0.761745\
A&=\sin^{-1}(0.761745)\approx49.6^{\circ}\approx50^{\circ}
\end{align*}
$$
## Step3: Use the angle - sum property of a triangle to find angle $B$
The angle - sum property of a triangle states that $A + B+C=180^{\circ}$.
So $B=180^{\circ}-A - C$.
Substituting $A\approx50^{\circ}$ and $C = 98^{\circ}$ into the formula:
$$
\begin{align*}
B&=180^{\circ}-50^{\circ}-98^{\circ}\
B&=32^{\circ}
\end{align*}
$$

# Answer:
$c\approx9.1$, $A\approx50^{\circ}$, $B\approx32^{\circ}$

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QUESTION IMAGE

Question

Explanation:

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

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

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

Answer: