Final answer:
The radius of a semi-elliptical arch that is 42 ft across is 21 ft, as the 42 ft measurement represents the length of the major axis of the whole ellipse, and the radius is half of that axis.
Step-by-step explanation:
The student asked about the radius of a semi-elliptical arch that is 42 ft across. The key to solving this type of geometry problem lies in understanding the properties of an ellipse. A semi-ellipse is half of an ellipse, which can be thought of as a stretched out circle. The major axis of an ellipse is the longest diameter, and it passes through the center of the ellipse. In this semi-elliptical arch, the 42 ft measurement is the length of the major axis because it is the distance across the widest part of the arch.
Since the arch is semi-elliptical, this means we are only considering half of the ellipse. The major axis length would be the total width of a full ellipse. Therefore, the radius -- or half the distance across the major axis of the full ellipse -- would be half of 42 ft, which is 21 ft. In this scenario, the radius of the semi-ellipse is 21 ft, which corresponds to answer choice a) 21 ft.