A traveler comes upon a fork in the road.
On the path to the traveler's right, a sign reads "Mercer: 24\,\text{km}24km24, start text, k, m, end text."
On the path to the traveler's left, a sign reads "Turtle Lake: 17\,\text{km}17km17, start text, k, m, end text."
The traveler also observes that the angle between the paths is 75^\circ75
∘
75, degrees.
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.