Consult the figure. To find the length of the span of a proposed ski lift from A to B, a surveyor measures the angle DAB to be $25^{\circ}$ and then walks off a distance of $L=1750$ feet to $C$ and measures the angle $A C B$ to be $15^{\circ}$. What is the distance from $A$ to $B$ ? The distance from A to B is approximately $\square$ feet. (Do not round until the final answer. Then round to two decimal places as needed.)

Step 1 ：We are given a triangle ABC, where AC = 1750 feet, angle A = 25 degrees, and angle C = 15 degrees. We are asked to find the length of side AB.

Step 2 ：We can use the law of sines to solve this problem. The law of sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in a given triangle.

Step 3 ：Applying the law of sines, we get the equation: \(\frac{AB}{\sin(25)} = \frac{1750}{\sin(15)}\)

Step 4 ：Solving for AB, we get: \(AB = \frac{1750 \cdot \sin(25)}{\sin(15)}\)

Step 5 ：Calculating the above expression, we find that AB is approximately 2857.53 feet.

Step 6 ：Final Answer: \(\boxed{2857.53}\) feet