Question

What is the exact length of AB

Answer 1

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

Answer 2

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

$Arc \; Length = 2 \pi r \frac{\theta}{360^{\circ}}$

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

$Arc \; Length = 2 \pi *4 *\frac{45^{\circ}}{360^{\circ}}$

$Arc \; Length = 2 \pi *4 *\frac{1}{8}$

$Arc \; Length = 8 \pi *\frac{1}{8}$

$Arc \; Length = \pi$

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