a ship travels 60 miles in the direction s 45° e, then travels 150 miles in the direction s 20° w. what is the distance, x, from the starting location?
135.99 mi
149.32 mi
172.93 mi
183.60 mi

Question

Accepted Answer

# Answer:
C. 172.93 mi

# Explanation:
## Step1: Find the included angle
The included angle between the two paths is $45^{\circ}+ 20^{\circ}=65^{\circ}$

## Step2: Apply the Law of Cosines
The Law of Cosines formula is $x^{2}=a^{2}+b^{2}-2ab\cos C$, where $a = 60$, $b=150$, and $C = 65^{\circ}$

Substitute the values:
$$
\begin{align*}
x^{2}&=60^{2}+150^{2}-2\times60\times150\times\cos(65^{\circ})\
x^{2}&=3600 + 22500-18000\times0.4226\
x^{2}&=3600+22500 - 7606.8\
x^{2}&=26100-7606.8\
x^{2}&=18493.2\
x&=\sqrt{18493.2}\
x&\approx172.93
\end{align*}
$$

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QUESTION IMAGE

Question

Explanation:

Step1: Find the included angle

Step2: Apply the Law of Cosines

Answer: