Explanation for Question 23 From the Math (Calc) Section on the 2018 March Sat
Question 23 says in the figure above sign of 90 degrees, 2 minus X degrees is equal to 12 over 13. 3 What is the value of sign X degrees? 4 And I've gone ahead and I've written out that sign is equal to opposite. 5 Over-hype hot news. So what it tells us that sign 90 degrees 6 minus X degrees equals 12 of over 13. 7 That's telling us that sign of this angle, 8 we'll call this Y is 12 over 13. 9 And we know that because a triangle has 180 total degrees, 10 and we know that this side is 90 degrees. 11 So minus 90, that tells us that the remaining two angles, 12 Y and X equal 90. 13 So that means that 90 minus X is equal to 14 Y. So sign of Y is equal to 12 over 13. 15 Well, the opposite or the opposite side is right here. 16 So we know this is 12 and the high partners is here. 17 So we know that that's 13. Now we can plug those numbers into the 18 theorem, which is a squared plus B squared 19 equals C squared, C being the high pot news to figure out what the 20 third angle side is. And I'm just going to change this into C squared 21 minus a squared equals V square. 22 So 169 or 13 squared minus 23 144, which is 12 squared is equal to X 24 squared that tells us that 25 is equal to X squared. 25 And when we square root both sides, 26 the X is equal to five. 27 So now we know all three sidelines, we know five, 28 13, and 12, and finally we can find the sign of X. 29 So first we need to find the opposite side, 30 which is five. So that's the numerator. 31 And then we need to find the high partners, which is 13. 32 And we know that sine of X is just five over 33 13, or be.