A traveler comes upon a fork in the road.
On the path to the traveler's right, a sign reads "Mercer: $24\,\text{km}$."
On the path to the traveler's left, a sign reads "Turtle Lake: $17\,\text{km}$."
The traveler also observes that the angle between the paths is $75^\circ$.
**Assuming both paths are perfectly straight, what is the distance between Mercer and Turtle Lake?**
*Do not round during your calculations. Round your final answer to the nearest tenth of a kilometer.*
[[☃ numeric-input 1]] $\text{km}$
