based on the sketch below, how far is joeys house from the park?
school
1.2 miles
40°
joeys
house
1.3 miles
park
not drawn to scale
0.74 mi.
0.86 mi.
2.21 mi.
2.35 mi.

Question

Accepted Answer

# Explanation:
## Step1: Apply the Law of Cosines
The Law of Cosines formula is $c^{2}=a^{2}+b^{2}-2ab\cos C$. Let $a = 1.2$, $b=1.3$, and $C = 40^{\circ}$.
## Step2: Substitute values into the formula
$$
\begin{align*}
c^{2}&=1.2^{2}+1.3^{2}-2\times1.2\times1.3\times\cos(40^{\circ})\
c^{2}&=1.44 + 1.69-3.12\times0.7660444431\
c^{2}&=3.13-2.390058662\
c^{2}&=0.739941338\
c&=\sqrt{0.739941338}\
c&\approx0.86
\end{align*}
$$

# Answer:
$0.86$ mi.

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QUESTION IMAGE

Question

Explanation:

Step1: Apply the Law of Cosines

Step2: Substitute values into the formula

Answer: