Explanation for Question 35 From the Math (Calc) Section on the 2019 April Sat
In 35, we were given a picture of this right triangle where sine of 2 this angle is equal to two over five. 3 If this side a C is equal to the square root of N 4 we want to find the value of N so first we can fill in 5 our information using this sign. 6 Fate is equal to two over five. So that means sign is 7 equal to opposite over high pot news. 8 So the opposite side is two and the hypotony is, 9 is going to be five. However, the picture tells us that the hypothesis 10 is equal to 10, so we have to multiply our ratio by two. 11 So instead of two, over five, we're going to have four over 10. 12 And now that hypotony is matches up. 13 So the opposite is going to be four in order for the hypotony is 14 to be 10. Now that we have two out of three sides 15 of a right triangle, we can use Pythagorean theorem to find the length of 16 AC. 17 So C squared equals a squared plus B squared or 18 10 squared is equal to four squared plus the other side. 19 So B is going to be B squared is going to equal 10 squared 20 minus four squared. If we subtract four squared from both sides and 21 then taking the square root B is equal to the square root of 10 22 squared, which is a hundred minus four squared, 23 which is 16 and a hundred minus 16 24 is equal to 84. So AC is equal to the square root 25 of eight for now. We just found a C equals a squared 26 of 84. And the question tells us that AC is equal to 27 the square root of N. So that means, 28 and is going to equal 84.