Question

how do I find the central angle for turn b?

Answer 1

We will to use the formula to a sector areaa, which is given for:

$A=r^2\theta/2$

Where r is the radius and θ is the central angle.

We can rewrite the formula to obtain the central angle like this:

$\theta=\frac{2A}{r^2}$

We replace with the values of the track:

$\theta=\frac{2\ast51\pi}{20\ast3^2}=\frac{17\pi}{30}$

Then we change radians to degrees:

$\frac{17\pi}{30}\ast\frac{180}{\pi}=102\text{ \degree}$

Then the correct answer is 102°.