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Question

Accepted Answer

# Explanation:
## Step1: Find the included angle
The mountain is inclined at $20^{\circ}$ to the horizontal. The angle between the tower and the hillside is $180^{\circ}- 20^{\circ}=160^{\circ}$

## Step2: Apply the Law of Cosines
The Law of Cosines formula is $c^{2}=a^{2}+b^{2}-2ab\cos C$, where $a = 179$, $b = 46$, and $C=160^{\circ}$

Substitute the values into the formula:
$$
\begin{align*}
c^{2}&=179^{2}+46^{2}-2\times179\times46\times\cos(160^{\circ})\
c^{2}&=32041+2116-16468\times(- 0.9396926)\
c^{2}&=32041 + 2116+16468\times0.9396926\
c^{2}&=34157+15472.77\
c^{2}&=49629.77\
c&=\sqrt{49629.77}\
c&\approx222.78
\end{align*}
$$

# Answer:
$222.78$

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QUESTION IMAGE

Question

Explanation:

Step1: Find the included angle

Step2: Apply the Law of Cosines

Answer: