Question

A traveler comes upon a fork in the road.

On the path to the traveler's right, a sign reads "Mercer: 24 km."
On the path to the traveler's left, a sign reads "Turtle Lake: 17 km
The traveler also observes that the angle between the paths is 75
Assuming both paths are perfectly straight, what is the distance between Mercer and Turtle Lake?

*must be in km

Answer 1

25.6 km

Explanation:

Khan Academy:

Answer 2

The distance between Mercer and Turtle Lake is 25.57 km

Explanation:

Law of cosines

When a triangle is defined by two of its sides and the angle formed by them, we can apply the law of cosines to know the third side. Being a and b the known sides and
`\alpha` the angle, we write the law of cosines as

`\displaystyle c^(2)=a^(2)+b^(2)-2ab\cos \alpha`

In our case:

`a=24 km,\ b=17 km ,\ \alpha=75^o`

`\displaystyle c^(2)=24^2+17^2-2(24)(17)\cos 75^o`

`\displaystyle c^(2)=653.804`

`\displaystyle c=25.57\ km`

The distance between Mercer and Turtle Lake is 25.57 km