Final answer:
To find the circumference of a circle with a given arc length and central angle, we can set up a proportion and solve for the circumference. The circumference is approximately 170.59 feet.
Step-by-step explanation:
To find the circumference of a circle, we can use the formula C = 2πr, where C is the circumference and r is the radius. In this case, we don't know the radius directly, but we do know the measure of the central internal angle ACCB, which is 85 degrees. The length of the arc AB is also given as 40 feet. We can use this information to find the radius.
The measure of the central angle divided by 360 degrees gives us the fraction of the circumference that the arc corresponds to. So, 85 degrees / 360 degrees = 17/72. We can set up a proportion:
17/72 = 40 feet / C
Cross-multiplying, we get:
C = (40 feet * 72) / 17
Simplifying, the circumference is approximately 170.59 feet.