Can someone please help me with finding the measure of a central angle of a circle please?? Also finding the arc length between two points. Im completely lost.

Question

amistre64 · Answer

can you provide an example?

anonymous · Answer

Well I have to find the central angle of a ferris wheel that has a diameter of 150 meters

anonymous · Answer

I also have to find the arc length between each car of the ferris wheel, there are 28 cars

amistre64 · Answer

28 cars, divides a full circle into how many arcs?

anonymous · Answer

If I can find the answer to one of those questions I can get the other one by myself lol

anonymous · Answer

ummm it divides it into 28 arcs, correct?

amistre64 · Answer

right

so,360 degrees is a full circle,  divided into 28 arcs ... what is 1/28th of 360?

anonymous · Answer

about 12.86

amistre64 · Answer

so the angle from car to car is about 12.86

amistre64 · Answer

degrees

amistre64 · Answer

the arc length is just 1/28th of the circumference ... how do we determine the circumference of a circle?

anonymous · Answer

ohhhhh okay, let me figure out the central angle and see if I get the correct answer :)

anonymous · Answer

the circumference is 471.24

anonymous · Answer

because 2pi(75) = 471.2389

amistre64 · Answer

2(75) = 150 ... d*pi is another way to express 2pi r

amistre64 · Answer

so yeah

150pi/28  should be the arc length

anonymous · Answer

that gives me 16.83

amistre64 · Answer

yep

amistre64 · Answer

keep in mind that for the central angle, if they want radians ... that would be 2pi/28

anonymous · Answer

So, i thought I would be able to find the central angle measure on my own but I was wrong lol. How would I be able to find the central angle measure with the arc length?

anonymous · Answer

And thank you so much for helping me

amistre64 · Answer

well...

2pi r/28 is arclength

and 2pi/28 is that radian angle ...

2pi r/28r

arclength divided by r gives radian measure of angle

amistre64 · Answer

good lcuk

anonymous · Answer

I got .2244

anonymous · Answer

So would I move the decimal over 2 places?

amistre64 · Answer

.2244 radians is correct, no need to move anything

anonymous · Answer

oh.. okay, soooooo my central angle measure is .23 and my arc length is 16.83? :)

amistre64 · Answer

seems fair to me

amistre64 · Answer

or 360 degrees/28 gives us the degree of the angle instead of the radian

anonymous · Answer

Thank you so much! You're a life saver!

amistre64 · Answer

yw