Explanation for Question 11 From the Math (No Calc) Section on the 2019 April Sat
For a number of 11, we are given this triangle in the picture. 2 Then we are also given that X is equal to 60. 3 So this angle here is 60 degrees. 4 And we have looking for side a B, 5 which is the hypotenuse of the triangle. 6 So the first step to find a B, we would want to find this 7 missing angle here. I'm a call it Y since X is already taken, 8 we know all of the angles in a triangle have to add up to 9 180 degrees. So that means Y plus 60 plus 10 90, we know that's a right angle because it tells us it's a right 11 triangle. All of that has to add up to 180. 12 So first on subtract 90 from both sides that gives me Y plus 13 60 equals 90, 14 and then subtracting 60 leaves you with Y equals 15 30. So this last angle here is 30 degrees. 16 So now if you have 30, 60, and 90 as angles in a triangle 17 that should start ringing some bells and remind you of this best, 18 the special 30, 60, 90 triangle. 19 The reason it's special is because the ratios of the sides are always consistent. 20 As long as the angles are 30, 21 60, and 90. So those ratios are the smallest side 22 is X. Then the Highpoint news is two X. 23 And the longer base is X times root three. 24 You know which base is which, because the smaller one corresponds to the smaller 25 angle and the larger base corresponds to the larger angle. 26 So X is always going to be directly opposite from 30 degrees 27 and expert three is always going to be directly opposite from 60 degrees. 28 So I drew this triangle on its side so that it would 29 match the way that the triangle given in the question is set up and 30 that'll make it a little bit easier to start matching up the sides. 31 So it gives us this four, 32 which matches up with this X. So now we know X is equal to 33 four. And if we are looking for the high partners, 34 we know that that is two X. So if X is equal to four, 35 that means I have partners is going to be two times four, 36 which is eight. And that is B.