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=(2A)/(r^2)`

We replace with the values of the track:

`\theta=(2\ast51\pi)/(20\ast3^2)=(17\pi)/(30)`

Then we change radians to degrees:

`(17\pi)/(30)\ast(180)/(\pi)=102\text{ \degree}`

Then the correct answer is 102°.