If you're seeing this message, it means we're having trouble loading external resources on our website.

Хэрэв та вэб шүүлтүүртэй газар байгаа бол домэйн нэрийг *.kastatic.org and *.kasandbox.org блоклосон эсэхийг нягтална уу.

Үндсэн товъёог
Цаг: 0:00Нийт үргэлжлэх хугацаа:2:39

Video transcript

P is the center of the green arc so this is P right over here the measure of angle P is 0.4 radians and the length of the radius is 5 units the length of the radius is 5 units that's this length right over here find the length of the green arc so just to kind of conceptualize this a little bit P you could imagine as the center of this larger circle is a larger circle and this angle right over here that has a measure of 0.4 radians it intercepts this a green arc right over here in order to figure this out and actually I encourage you to pause this video now and try to think about this question on your own how long is this arc given the information that they've given us well all we have to do is remind ourselves what a Radian is one way to think about a Radian is if you look at the arc that the angle intercepts which is this green arc and you think about its length the length of this green arc is going to be 0.4 radii one way to think about radians is if this if this angle is 0.4 radians that means that the arc that it intercepts is going to be 0.4 radii long so this length we could write a 0.4 radii radii or radius assistance but radii is the proper term now we don't want our length in terms of radii we want our length in terms of whatever units the radius is this these kind of five units well we know that each radius has a length of five that our radius of the circle has a length of five so this is going to be 0.4 radii times five and you know they just call it units right over here times five I'll put it in quotes because it's kind of a generic term five units per / radii so what's so the radii cancel out we're left with just the units which is what we want so 0.4 times 5 is 2 so this is going to give us this is going to be equal to two so just as a refresher again that when the the angle measure in radians one way to think about it is the arc that it intercepts that's going to be this many radii long well if each radius is five units it's going to be zero point four times five units long or two