Circle o has a radius of 10. Length of AB = pi/4. How many degrees is angle AOB?

Question

anonymous · Answer

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aum · Answer

Arc length = $r\theta$
$\pi/4 = 10\theta$.
Find $\theta$.  It will be in radians.
Multiply by $180/\pi$ to convert the angle to degrees.

campbell_st · Answer

which part is causing you a problem..?

anonymous · Answer

The whole thing. I forget how I am supposed to be doing this

campbell_st · Answer

ok...the arc length AB is given to you in terms of pi... so the angle measure used was radians... not degrees... so once yo know the angle... which will be in radians you'll need to convert it. 

so the formula for arc length is 

$$l = r \times \theta$$

you know l and r so 

$$\frac{\pi}{4} = 10 \times \theta$$

make theta the subject and then 

$$\theta  = \frac{\pi}{40}$$

so that is the angle measure in radians... is that ok..?

anonymous · Answer

yep.. thanks!

campbell_st · Answer

ok... lastly the angle conversion.... 

you need to know 

$$\pi = 180^0$$

so substituting, the angle in degrees is 

$$\theta = \frac{180}{40}$$ 

just calculate it.