analyzing-relationships-a-45circ-arc-in-odot-mathrmc-and-a-length-of-mathrmpq-to-the-length-of-rs-is

Question

ANALYZING RELATIONSHIPS  A $45^{\circ}$ arc in $\odot \mathrm{C}$ and a length of $\mathrm{PQ}$ to the length of RS is 2 to $1 .$ What is the ratio of $m \angle \mathrm{PCQ}$ to $\mathrm{mL} \mathrm{RCS}$ ?

Georgiann Andersen · Accepted Answer

you were doing problem number 32 and we know on this one they&#x27;re the radius of Circle C is equal to our one. We also know that the radius of Circle P it&#x27;s our two, the Ark major and Circle C. It&#x27;s 45 degrees the ark major and Circle P is 30 degrees. Hey, we also know that the arc length the Ark links are equal. Okay, so we know that the arc length we can take 45 degrees over 360 degrees times to pie are one, and we can make that equal to 30 degrees over 360 degrees. Times to pie are too. Okay, so we can cancel out a couple of the same factors so we can get rid of that three sixties. We can get rid of the two pi leaving us with 45 degrees. 45 are one equals 30 are too. So we want to get the ratio of our one toe are too. So we need to get the R two over the other side and the numbers to the ah, the right side. So to do that, we can divide by 45 and that&#x27;s gonna leave us with Our one equals 30. 45th times are too. Now we can divide by the art too. And that&#x27;s gonna leave us with our one over. Our two equals 30 over 45. Let&#x27;s reduce this down. And that&#x27;s gonna leave us with our one over. Our two equals two thirds. So our ratio ISS of one are one toe are two is 2 to 3, so we can even leave it. Leave it as written to over three, or we can say 223

Joseph Lentino · Answer

in this problem were asked to find the length of a narc. So there&#x27;s my circle. We know that there&#x27;s a central angle of 45 degrees. We also know that the radius of the circle is 10 meters were trying to calculate this distance around the outside of the circle. So one of the things that we know is that arc length is equal to the radius times the radiant measure in this case. So our data in this case we know the radius is 10 meters. We know that the angle measure is 45 degrees. If I convert 45 degrees to radiance, that would be 45 degrees over one times pi over 1 80 this would simplify two pi over four. When I put Pi over four in for the radiant measure and I multiply, I&#x27;m going to get 10 pi over four, which will simplify to five pi over two meters. This is the arc length on the circle

Ethan Somes · Answer

So here we have a circle, um, Circle P and we haven&#x27;t angle. Q p r. And it&#x27;s a right angle tonight degree angle. And we know the radius is 16. Um, so let&#x27;s find the length of Q r. Mark you are. So that will be the radius times. The central angle in radiance now 90 degrees in readings is pi over two. So I&#x27;m gonna do 16 times pi over two. Um, so 16.5 or two will be ate pie and eight pine. It is approximately equal to 25.13

K B · Answer

So here we&#x27;re gonna be using our formula s equals our data to find the ark. So we know that our radius it is given as to be equal to two. And then we&#x27;re given that our angle is 60 but we have 60 degrees. So to convert this to radiance, we must have a pie over one. He let me see that. That&#x27;s gonna be pi over three just by canceling like this. So what we got is your solution is to pilot three for the ark.

Rishi Kavikondala · Answer

sq by sex R S t. So let&#x27;s draw that SP by sex rs Q and S V by sex R S p. So everything in this problem seems to be centering around a line where the center is s and you have an angle are or appoint our and we&#x27;re told that the measure of angle the S P is equal to 17 degrees. So, sq by sex rst So let&#x27;s draw t Here is a cue. So that means these two angles are equal S p by sex rs cute. So that means we have a bisect her right here and s v by sex rs Pete. So right here we have another by sector. All right, so let&#x27;s go through and find which angles are equal. We know that Q t s R. Q S T and QS are equal. We know that p S r and Q S P are equal and we know psr and oh, actually, we just mentioned that we know that V S, R and P S V are equal and we&#x27;re told P S V is 30 for Earth 17 degrees. So if the measure of angle B s ps 17 then the measure of angle R s V should also be 17. Therefore, the measure of angle P S R should be 34 because you&#x27;re just adding these two together. We&#x27;re trying to find t s cute. That&#x27;s what we&#x27;re ultimately trying to find. So we know what PSR is. If S P is a by sector of que es are, then that means that the angle Q s P should be 34 degrees as well. Therefore, angle Q. S r is going to be 34 plus 34 which is 68. And because angle QSR 68 Angle T s Q is equivalent to that since que esses abi sector, we can conclude that the measure of angle T s Q is equal to 68 degrees. This is a degree symbol here.

Lily An · Answer

So, first of all, it&#x27;s kind of like Mark, what were even looking for. So we&#x27;re looking for Q and R. That&#x27;s this angle right here. That&#x27;s that&#x27;s like what we&#x27;re looking for. So then that sort of fill in all of the rest. So for the mouth section of the A. C as eighty, we know that we&#x27;re going to be using every single piece of information that they give us. So let&#x27;s try to think about what this represents here, so I&#x27;m Q is on our. If it&#x27;s like this, this is the same. Ask this because it interesting point P and empty in q P are the same, and MP and P are the same. That means if this and this are the same, that means that this triangle is a nice sauce lease. Tribal. So that means that if this side and this side of the same this side and this angle or this England, this evil must also be the same. I&#x27;m going to go and call that X, and this is also X. But then we can notice that over here my guess is that angle a sixty degrees, which means at this angle must be one. Eighty minus is sixty degrees because we know that the angle measure of a straight line is one hundred eighty degrees. That&#x27;s going total to one hundred and twenty degrees. Okay, so from here, we know that the total sum for a triangle is equal to one eighty degrees. So one eighty degrees must be the total of one twenty Therese Oops, plus the X and the ex. And we&#x27;re gonna go ahead and call that too x. So now we have this situation here. So in order to isolate our accent, who&#x27;s going to subtract one twenty from both sides, giving us sixty and then that is equal to X. And then finally, to isolate Max, I&#x27;m going to divide both sides by two. Giving us that X is equal to thirty Greece. So then that means Q R is thirty degrees

Problem

PROBLEM SOLVING HOW many revolutions does the sma…

Problem 32 Hard Difficulty

ANALYZING RELATIONSHIPS A $45^{\circ}$ arc in $\odot \mathrm{C}$ and a length of $\mathrm{PQ}$ to the length of RS is 2 to $1 .$ What is the ratio of $m \angle \mathrm{PCQ}$ to $\mathrm{mL} \mathrm{RCS}$ ?

Answer

$\frac{r_{1}}{r_{2}}=\frac{2}{3}$

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$\frac{r_{1}}{r_{2}}=\frac{2}{3}$

Geometry A Common Core Curriculum

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Megan C.

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