Explanation for Question 19 From the Math (No Calc) Section on the Official Sat Practice Test 1
So number 19 tells us the inner right triangle. 2 So we can draw a triangle up here with a right angle, 3 one angle measure, X degrees, 4 and the sine of X is four over five, 5 right? So we know that sign is opposite overhead plot news. 6 So the opposite of X would be four and our hypo news would be 7 five. And then they want to know what is the co-sign of 90 minus 8 X. And so first I'll show you the way that you can do this 9 mathematically. And then in the end, you'll realize that this is a really common 10 pattern and it actually gets tested quite frequently on the sat as though this 11 is just something that you can kind of remember as well. First thing we 12 noticed is that we've changed from looking for the sign to looking for the 13 co-sign. Second thing we can notice here is that we have 14 X and we're doing 90 minus X, 15 right? 16 So if we think about a triangle, let's call this, 17 Y we can think about how a triangle is equal to 180, 18 right? All the angles add up to 180. So 90 for our 90 degree 19 angle here, plus X plus Y would be equal to 180. 20 Now, if I subtract 90 from both sides, get rid of that 90, 21 I get that 90. 22 And then these cancel is equal to X plus Y. 23 And so 90 minus X, right? I track X from both sides. 24 90 minus X is equal to our angle of Y. 25 So really they just want to know what is the co-sign of angle Y 26 right here. And we can remember that co-sign is adjacent. 27 Over-hype hot news, right from sohcahtoa. Our adjacent is for our hyp...