jims puppy jumped out of the house. it ran 14 yards, turned and ran 7 yards, and then turned 140° to face the house. how far away from the house is jims puppy? round to the nearest hundredth.

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Accepted Answer

# Explanation:
## Step1: Identify the formula
We use the Law of Cosines. For a triangle with sides $a$, $b$, $c$ and the angle $C$ opposite to side $c$, the formula is $c^{2}=a^{2}+b^{2}-2ab\cos C$. Here $a = 14$, $b = 7$, and $C=140^{\circ}$.
## Step2: Substitute the values
$$
\begin{align*}
c^{2}&=14^{2}+7^{2}-2\times14\times7\times\cos(140^{\circ})\
c^{2}&=196 + 49-196\times\cos(140^{\circ})
\end{align*}
$$
We know that $\cos(140^{\circ})\approx - 0.766$.
$$
\begin{align*}
c^{2}&=196+49-196\times(-0.766)\
c^{2}&=245 + 149.136\
c^{2}&=394.136
\end{align*}
$$
## Step3: Find the value of $c$
$$c=\sqrt{394.136}\approx19.85$$
# Answer:
19.85

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Question

Explanation:

Step1: Identify the formula

Step2: Substitute the values

Step3: Find the value of \(c\)

Answer: