Question

A traveler comes upon a fork in the road.

Answer 1

Answer:

The distance between Mercer and Turtle Lake is 25.57 km

Step-by-step 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