Explanation for Question 36 From the Math (Calc) Section on the Official Sat Practice Test 4
So now for number six, we're given a circle, 2 right? And we're told that our radius is 10 and that the length of 3 this arc right here is between five and six. 4 And so we're really going to be using the equation for arc length, 5 which is S or SS arc length is 6 equal to R for ours, your radius times data, 7 right? We're fate is your ankle measure. And what's important to know is that 8 it's in radians, not through grease, 9 right? So if we are looking here and we're going to use this equation 10 essentially to solve for our ankle measure, 11 right? So we're interested in solving for theta. 12 We can use our lower and upper bound of the arc length to come 13 up with one or even more numbers possible angle measures for our circle. 14 So let's use the example of where the arc length is, 15 five right. S would be equal to five and that's equal to 10 times 16 data. So if I solve for theta, 17 I guess the theta is equal to one half, 18 but it's important to know that, um, that feta is actually in radians, 19 right? So if I have 0.5 is my radiance, 20 and we know that we need to cancel out the radians, 21 right? So PI radians is equal to 180 degrees. 22 Then if I do 0.5 divided by PI times 180, 23 I'll get my angle measure. 24 So I'll plug that on my calculator. Point five divided by PI times 180, 25 and I get 28.6, 26 four degrees. So that's my lower bound here, 27 28.64 degrees, 28 because that's what I got is my lower bound. Cause that's what I got 29 when I used my lowest pos...