Rationale
178 cm is the appropriate estimate of a person's height of 5 feet, 10 inches.
To convert a height of 5 feet, 10 inches into centimeters, we first convert the feet to inches and then multiply the total inches by 2.54 cm. The calculation yields 178 cm as the accurate conversion.
A) 28 cm is significantly lower than the actual height of 5 feet, 10 inches. This value does not account for the conversion from feet and inches to centimeters. Each foot is equivalent to 30.48 cm, and therefore 28 cm is an incorrect estimate.
B) 85 cm is also an inaccurate estimate of height. While it is closer than 28 cm, it still fails to encompass the full conversion from feet and inches. 85 cm is equivalent to approximately 33.5 inches, whereas 5 feet, 10 inches converts to 70 inches, making this choice incorrect.
C) 178 cm is the correct conversion for a height of 5 feet, 10 inches. First, we convert 5 feet to inches (5 feet × 12 inches/foot = 60 inches) and then add the remaining 10 inches, resulting in 70 inches. Finally, multiplying 70 inches by 2.54 cm/inch gives us 178 cm.
D) 152 cm is not an appropriate estimate either. This height is less than 5 feet tall, as 152 cm is approximately 59.84 inches. The original height of 5 feet, 10 inches (70 inches) exceeds this measurement, marking it as incorrect.
Conclusion
The conversion of 5 feet, 10 inches to centimeters results in a height of 178 cm, making option C the only accurate choice. The other options misrepresent the height by not properly converting feet and inches to centimeters, leading to significantly lower or incorrect values. Understanding the conversion factor is crucial for accurate height assessments in different measurement systems.