Final answer:
The length of the outer curve of the road for railing installation, considering a 70-degree angle and a total radius of 70 feet (including the road's width), can be calculated as a proportion of the circle's circumference, yielding approximately 85.5 feet. However, as this result does not match the provided options, there might be an error in the question or the answer choices.
Step-by-step explanation:
The student has asked about finding the length of the outer curve of a road for the purpose of installing a railing.
The information provided is that the road is 20 feet wide, the outer side of the path is 50 feet away from a marked point, and there is an angle of 70 degrees.
To find the length of the outer curve, we can use the formula for the circumference of a circle (C = 2πr) and adjust it for the portion of the circle represented by the 70-degree angle.
First, we calculate the full circumference using the radius which includes the road width, so r = 50 feet + 20 feet = 70 feet.
This gives us the circumference C = 2 x 3.14 x 70 feet = 439.6 feet. Since the 70-degree angle represents 70/360 of the full circle, we calculate the length of the outer curve as (70/360) x 439.6 feet, which gives us approximately 85.5 feet.
However, since none of the given options are close to this result, it seems there may be a mistake in the interpretation of the question's information or the provided answer options.