3. A lighthouse is east of a Coast Guard patrol boat. The Coast Guard station is $20 \mathrm{~km}$ north of the lighthouse. The radar officer aboard the boat measures the angle between the lighthouse and the station to be $23^{\circ}$. How far is the boat from the station?

Step 1 ：Form a right triangle with the boat, lighthouse, and station. Let the distance between the boat and the lighthouse be y, and the angle between the boat and the lighthouse be A. Use the tangent function: \(\tan(A) = \frac{20}{y}\)

Step 2 ：Use the Pythagorean theorem to find y: \(y^2 + 20^2 = x^2\). Solve for A and y, and then use the Law of Sines to find x: \(\sin(A) / 20 = \sin(180 - 23 - A) / x\)

Step 3 ：\(x \approx 21.57\)

Step 4 ：\(\boxed{21.57}\)