jims cat jumped out of the kitchen. it ran 23 yards, turned and ran 16 yards, and then turned 130° to face the kitchen. how far away from the kitchen is jims cat? round to the nearest hundredth.

Question

Accepted Answer

# Explanation:
## Step1: Identify the problem as a triangle - side - finding problem
We can use the Law of Cosines. The Law of Cosines formula is $c^{2}=a^{2}+b^{2}-2ab\cos C$, where $a = 23$, $b = 16$, and $C=180^{\circ}- 130^{\circ}=50^{\circ}$

## Step2: Substitute the values into the Law of Cosines formula
$$
\begin{align*}
c^{2}&=23^{2}+16^{2}-2\times23\times16\times\cos(50^{\circ})\
c^{2}&=529 + 256-736\times0.6428\
c^{2}&=529+256 - 473.0928\
c^{2}&=785-473.0928\
c^{2}&=311.9072
\end{align*}
$$

## Step3: Solve for $c$
Take the square root of both sides: $c=\sqrt{311.9072}\approx17.66$

# Answer:
$17.66$ yards

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QUESTION IMAGE

Question

Explanation:

Step1: Identify the problem as a triangle - side - finding problem

Step2: Substitute the values into the Law of Cosines formula

Step3: Solve for \(c\)

Answer: