Explanation for Question 20 From the Math (No Calc) Section on the Official Sat Practice Test 3
Now number 20, we're given a triangle ABC, 2 right? So we'll draw this out. A, B, 3 C, where B is 90. 4 So maybe I'll draw this a different way since we know that B is 5 90, I'll draw it to look like this. 6 So here's 90 B and then we're told that BC is 7 16 and AC is 20, 8 and that triangle Def is similar. 9 Right? And so when they say similar, that means that we have the same 10 angle measures, but different side blanks. 11 So E will also be D E F D 12 or you will also be 90 degrees and yes, 13 yes, yes. Okay. And each side, like the F is one third, 14 the length of a corresponding angle, right? So essentially if we're one third of 15 the length, then that means that side F E would be 16 divided by 16 three, and this side would be 20 divided by three. 17 Um, and then they ask us, what is the sign of F sign of 18 F? And so the important thing here is that you really don't even need 19 to know the side blanks on this, 20 uh, triangle, right? Because, 21 um, we can just use the side links on the bigger triangle, 22 because sign of F is the same thing as the sign of C because 23 F and C have the same angle measures, 24 right? And the same angle measure means the same sign. 25 So essentially we need to find the sign of C, 26 which is opposite over hypotenuse, but we don't know what the opposite is. 27 And so we need to do some Pythagorean theorem in order to do that. 28 Um, so we'll have 16 squared plus we'll call it O oh, 29 squared is equal to 20 squared. If we do the 16 times...