use the law of sines to find the indicated side length in this triangle. round your answer to the nearest hundredth.

Question

Accepted Answer

# Explanation:
## Step1: Find the third angle
The sum of angles in a triangle is $180^{\circ}$. Let the unknown angle be $A$, then $A = 180^{\circ}-88^{\circ}-29^{\circ}=63^{\circ}$.
## Step2: Apply the law of sines
The law of sines states $\frac{a}{\sin A}=\frac{b}{\sin B}$. Let the side opposite $88^{\circ}$ be $x$, the side opposite $29^{\circ}$ is $16$. So $\frac{x}{\sin88^{\circ}}=\frac{16}{\sin29^{\circ}}$.
## Step3: Solve for $x$
$$
\begin{align*}
x&=\frac{16\times\sin88^{\circ}}{\sin29^{\circ}}\
\sin88^{\circ}&\approx0.9994\
\sin29^{\circ}&\approx0.4848\
x&=\frac{16\times0.9994}{0.4848}\
x&=\frac{15.9904}{0.4848}\
x&\approx32.98
\end{align*}
$$

# Answer:
$32.98$

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QUESTION IMAGE

Question

Explanation:

Step1: Find the third angle

Step2: Apply the law of sines

Step3: Solve for \(x\)

Answer: