How do I find the central angle for turn b?

Question

asked Apr 11, 2023 156k views

1 Answer

Peter Tran · Answer 1 · 2023-04-17T12:42:18+0000

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°.