a canoe is seen floating down a river. the canoe is first spotted 60 feet away. a few moments later the canoe is 35 feet away, making a 45° angle between the two sightings. how far did the canoe travel? round to the nearest tenth.

Question

Accepted Answer

# Explanation:
## Step1: Apply the Law of Cosines
The Law of Cosines formula is $c^{2}=a^{2}+b^{2}-2ab\cos C$. Here, $a = 60$, $b=35$, and $C = 45^{\circ}$, and we want to find $c$ (the distance the canoe traveled).
$$
\begin{align*}
c^{2}&=60^{2}+35^{2}-2\times60\times35\times\cos(45^{\circ})\
c^{2}&=3600 + 1225-4200\times\frac{\sqrt{2}}{2}\
c^{2}&=4825-2100\sqrt{2}\
\end{align*}
$$
## Step2: Calculate the value of $c$
$$
\begin{align*}
c^{2}&=4825-2100\times1.4142\
c^{2}&=4825 - 2969.82\
c^{2}&=1855.18\
c&=\sqrt{1855.18}\
c&\approx43.1
\end{align*}
$$

# Answer:
$43.1$ feet

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Apply the Law of Cosines

Step2: Calculate the value of \(c\)

Answer: