Explanation for Question 6 From the Math (No Calc) Section on the 2017 October Sat
Question six says the circle above has sent her. 2 Oh, the length of RDC is five PI and X is 3 equal to a hundred. What is the length of arc? 4 A, B, C. So what we have to do here is take this equation 5 that I've already written out X over 360 times two PI R is equal 6 to our claim. We need to plug in the information we've been given in 7 the problem and find the radius. 8 And after we find the radius, we're going to insert that into the equation 9 and solve for our ABC. So let's just start by plugging 10 in the information. We know, we know that X is equal to 100. 11 So I'm going to fill that in. And we know that the arc length 12 is equal to five PI. 13 So now we can use this to solve for X. 14 Well, we know that a hundred over 360 can simplify to 10 15 over 36 and again to five over 16 18. 17 So that times two PI R is equal to five PI. 18 We can also rewrite this as 10 PI 19 R over 18 is equal to five PI. 20 Now we need to divide both sides by 10 PI over 18, 21 which is the same as multiplying both sides by 18 over 10 PI. 22 And that gives us 18 over two is equal to R. 23 So we know that R is equal to nine. 24 So now that we know that R is equal to nine, 25 we can just find what the inner angles equal to. 26 And then we have the radius and the inner angle, 27 and we can plug that information again into this original equation to find the 28 length of arc. ABC, since circles have an inner degree of 29 360 degrees, and we know that COA angle COA 30 or X is a hundred degrees....