Question

What is the exact length of AB

Answer 1

To find value of arc AB, we just need to apply arc lenght formula

`Arc \; Length = 2 \pi r (\theta)/(360^(\circ))`

Plug the given values of radius r = 4 angle theta = 45

`Arc \; Length = 2 \pi *4 *(45^(\circ))/(360^(\circ))`

`Arc \; Length = 2 \pi *4 *(1)/(8)`

`Arc \; Length = 8 \pi *(1)/(8)`

`Arc \; Length = \pi`

So the final answer is
`Arc \; Length = \pi`

Answer 2

We have the formula S= r * theta , where S is arc length , r is radius , and theta is central angle in radians

So AB= 4 * 45* π/180 = π units