Explanation for Question 16 From the Math (Calc) Section on the Official Sat Practice Test 6
Question 16 gives us these two triangles and it asks triangles, 2 ABC and Def are shown above which the following is equal to the ratio 3 BC over AB. Okay. 4 So BC is going to be right here and AB 5 is going to be right here. 6 Okay. So what we're going to want to do first is 7 figure out how these triangles are related to each other. 8 And I'll give you a key. Um, when we see triangles on the sat, 9 the first thing we want to check for is to see if they're similar 10 and we have similar triangles. If all of the angles are the same, 11 but we can say that we only had two out of the three angles 12 on both of these triangles. So let's try and find the third. 13 Now that all angles angles added together are equal to 180. 14 And let's look at ABC first. 15 So we know that 180 is equal to 32 plus 90 16 because this symbol means it's right triangle and a right triangle has 90 degrees 17 plus X with X being this unknown angle. 18 So it's fine that we've got 180 minus 30 to minus 90 X is 19 equal to 58. And that's great because we can see 20 right here that this angle is equal to 58. So we can start to 21 get the idea that they are similar triangles. So similarly for this 22 one, because we know that they all add up to 180. 23 We have 180 is equal to 58 plus 90 plus looks 24 at call it Y and again, 25 we can just solve and find out that this angle is equal to 32. 26 So these are in fact, similar triangles. 27 Now with similar triangles, their angles are the same, 28 but their length...