Explanation for Question 19 From the Math (No Calc) Section on the 2017 October Sat
Question 19 says triangle PQ R has right angle cue. 2 If sign of R is equal to four over five, 3 what is the value of tan P? 4 So the first thing I've done here is just drop this triangle. 5 So it's easier to visualize, uh, with cubing, 6 the right angle and line RP being the high pot news. 7 And then I wrote out that sign is equal to opposite over hypotenuse, 8 and that tan is equal to opposite over adjacent. 9 So now we can take the information we know and fill in some information 10 on the triangle. So we know that sign of art is four over five. 11 Now that means the opposite of a angle R is four and 12 the high pot news is five. 13 So I'm just going to write that in. This is the opposite side of 14 our, this is four and the hypotony is equal to five. 15 Then to find tan of P we go to angle P and we need 16 to find the opposite over the adjacent. 17 Well, we know that the adjacent is four, but we don't know what the 18 opposite side is. So we know that tan of P is X over 19 four. So now all we have to do is solve for X. 20 And the way we can do that is by using the theorem, 21 which is that a squared plus B squared is equal 22 to C squared and C represents this, 23 the length of the high pot news. So in this case, 24 we know I'm just going to read right this as X squared, 25 plus four squared is equal to five squared because five is 26 the length of the high partners and we're solving for X. 27 So that becomes X squared. Plus 16 is equal to 25. 28 X squared is equal to nine. 29 That's from subtracting 16 from both sides. 30 And then if you root both sides, you get X is equal to three. 31 So we know that the tan of P is just three over 32 four.