Explanation for Question 9 From the Math (No Calc) Section on the 2017 May Sat
For question nine, we do have to know a bit of a trick identities, 2 but sohcahtoa is going to help us figure this out. 3 So, so good. So it helps us find what sine of X co-sign 4 of X and tangent of X all equal to these 5 are just, um, letters that stand for the first, 6 the signposts enter tangent and then the side. 7 So first for sign, we use the first three letters we have sign 8 is equal to opposite over hypotenuse. 9 So we have signup. X is equal to opposite over hypotenuse. 10 Then the same thing for co-sign just with the next two letters or next 11 three letters. And that says co-sign is equal to adjacent. 12 Over-hype hot news. So co-sign of X is equal to adjacent over 13 hypotenuse. And then lastly, 14 tangent of X. So we use the last three letters stands for tangent as 15 equal to opposite over adjacent. 16 So tangent of X is equal to opposite over adjacent. 17 Now that's really what the question is asking us. 18 It says in the right triangle above the tangent of a is four over 19 three. So if the tangent of eight is four over three, 20 we know that from what we just learn, 21 tangent is equal to opposite over adjacent. 22 So opposite over adjacent is equal to four. 23 Over three. It's also equal to, 24 we look at this angle a so the opposite of angle a is 20, 25 but then the adjacent we don't know yet. So we're just going to leave 26 an X there. 27 Now, if we know that the tangent of eight is four over 28 three, and we have 20, but not the adjacent side. 29 So we ...