Which notation correctly represents 59 degrees, 17 minutes, and 30 seconds?

The correct representation of 59 degrees, 17 minutes, and 30 seconds in terms of angle measurement uses the appropriate symbols for degrees, minutes, and seconds. In this context, degrees are denoted by the symbol (°), minutes by the single quote (') symbol, and seconds by the double quote (") symbol.

The correct notation is, therefore, 59° for degrees, followed by 17' for minutes, and finally 30" for seconds. This means that the notation reflects the hierarchical structure of angular measurement, with degrees being the highest unit, followed by minutes, and then seconds.

This structured approach provides clarity in representing angles, which is crucial in various fields such as navigation, astronomy, and geometry. Using the correct symbols as expressed in option B maintains this clarity and ensures that the measurement is universally understood. Hence, the notation 59°17'30" conveys the intended value accurately.