A driver is travelling along a straight highway with two prominent landmarks, Landmark X and Landmark Y. While driving, the driver notices something fascinating. After covering a distance of 300 metres from Landmark X, he observes that the angle of elevation to the top of Landmark X is 45 degrees, and the angle of elevation to the top of Landmark Y is 30 degrees. If Landmark Y has a height of 100 metres, determine the horizontal distance (in metres) between the tops of both Landmarks X and Y.

Using the 45-degree angle of elevation and the 300-meter distance, the height of Landmark X is 300 meters. From the same observation point, the horizontal distance to the base of Landmark Y is found using the tangent of 30 degrees, where 100 divided by the distance equals 1 divided by the square root of 2, making the distance 173.205 meters. The total horizontal distance between the landmarks is the sum of the 300 meters and the 173.205 meters, giving 473.205 meters. Using the Pythagorean theorem, the square of the distance between their tops equals the horizontal distance squared plus the difference in their heights squared, which is 473.205 squared plus 200 squared, resulting in a distance of 513.73 meters.

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