Explanation for Question 19 From the Math (No Calc) Section on the Official Sat Practice Test 9
Question 19 asks us triangle. 2 PQR has right angle cue. 3 If sign R is equal to four-fifths, 4 what is the value of tan P? Okay. 5 So I like to start these problems by always drawing a picture. 6 We've got, we know that it has a right angle of cue and triangle 7 PQR. So let's draw it like P Q, 8 R, and note that you could flip the R in the P. 9 Now let's write out our expressions for sign co-sign 10 and tan. We've got so, 11 uh, tow, 12 uh, so that means that sign is equal to opposite. 13 Over hypotenuse co-sign is equal to adjacent 14 over-hype hot nous and tan is equal to opposite 15 over adjacent. So we know that sign R is 16 equal to, excuse me, 17 sign of angle R is equal to four over five. 18 So four over five is equal to opposite of our 19 over-hype hot news. So the hypotony is, 20 has gotta be equal to five and then opposite from our, 21 we can just draw a straight line out from R and we can see 22 that this side right here is equal to four. 23 Now quickly, we can hopefully see that this is a 3, 4, 5 triangle. 24 So when you have a right angle right here, 25 and when you already know to the side lengths, 26 it's a special type of triangle where you've got a right angle and it's 27 going to be 3, 4, 5. And those three, 28 that three in the form would be switched. But the five is always on 29 the hypotony news. So from there, 30 we want to find tan of Pete. 31 Now I'm going to make a quick note right now that if you didn't 32 remember the 3, 4, 5 triangle trick, that's...