Answer:
Arc AB length = 19.55 m
Explanation:
We can find arc length using the following formula:
S = rθ, where
- S is the arc length,
- r is the radius of the circle,
- and θ is the measure of the central angle in radians.
Step 1: Convert 140° to radians:
We can convert 140° to radians by multiplying it by π / 180°:
(140°)(π / 180°)
140°π / 180°
7π/9 radians
We can leave the answer in terms of pi since the numerical order has numerous digits.
Step 2: Find the length:
The radius of the circle is 8 m. Now we can plug in 8 for r and 7π/9 for θ to find S, the length of arc AB:
S = (7π/9)(8)
S = (56π)/9
S = 19.54768762
S = 19.55
Thus, the length of the arc is about 19.55 m.