Explanation for Question 16 From the Math (No Calc) Section on the 2018 March Sat
Question 16 says in right triangle, 2 ABC above BC equals eight. 3 If the co-sign of X degrees is root three over two, 4 what is the length of line a B? 5 Now the co-sign of any angle is the adjacent side over the high pot 6 news. So we know that the adjacent side is route three and the high 7 pot news is two. However, 8 we know that the hypothesis is actually equal to eight, 9 which means that route three over two is going to be equal to Y 10 over eight with Y being the value of the adjacent side. 11 So if we cross multiply, we get eight, 12 route three is equal to two Y and it over to 13 route three, which is just four, route three is equal to Y. 14 So we know that the adjacent side, the side right here is equal to 15 four three. Now it's a fine, 16 the length of the opposite side. We can use the Pythagoras theorem. 17 So we know that this side we'll call this Y Y 18 squared plus four root three squared 19 is equal to eight squared, and we can rewrite this as Y 20 squared. Plus 16 times three 21 is equal to 64 and 16 times three is 22 30, 48. So Y squared plus 48 23 equals 64. 24 And then if we subtract 48 from both sides, 25 we get, Y squared is equal to 16 or Y is 26 equal to four. And so we know the length of this side AB is 27 four. And that's the correct answer here.