A boat is heading towards a lighthouse, where Jaxson is watching from a vertical distance of 103 feet above the water. Jaxson measures an angle of depression to the boat at point $A$ to be $12^{\circ}$. At some later time, Jaxson takes another measurement and finds the angle of depression to the boat (now at point $B$ ) to be $64^{\circ}$. Find the distance from point $A$ to point $B$. Round your answer to the nearest foot if necessary.

Step 1 ：Given that the height from Jaxson to the water is 103 feet, the angle of depression to the boat at point A is $12^{\circ}$, and the angle of depression to the boat at point B is $64^{\circ}$.

Step 2 ：We can use the tangent function to find the horizontal distances from Jaxson to the boat at points A and B. The tangent of an angle is the ratio of the opposite side to the adjacent side. In this case, the opposite side is the height (103 feet), and the adjacent side is the horizontal distance from Jaxson to the boat.

Step 3 ：Using the tangent function, we find that the horizontal distance from Jaxson to the boat at point A is approximately 484.5769012762808 feet, and the horizontal distance from Jaxson to the boat at point B is approximately 50.23645662228373 feet.

Step 4 ：We can find the distance from point A to point B by subtracting the horizontal distance at point B from the horizontal distance at point A. This gives us a distance of approximately 434.34044465399705 feet.

Step 5 ：Rounding to the nearest foot, we find that the distance from point A to point B is approximately \(\boxed{434}\) feet.