Explanation for Question 36 From the Math (Calc) Section on the 2018 May Sat
Question 36 says in the figure above ABC and DEC 2 are right triangles. If CD is equal to 20 and the tangent of 3 angle, ABC is 2.5. 4 What is the length of segment E D? 5 So I'm just going to fill in the information that I know to start. 6 I know that this side CD is equal to 20, 7 and then I'm going to name this angle X angle DEC. 8 And I know that these two angles, because these are similar triangles are equivalent 9 to each other, which means that the tan of this angle is the same 10 thing as the tan of angle X. 11 So when it says that the tan of angle ABC is 2.5, 12 I'm going to take that to mean that the tan of angle X is 13 also 2.5. So we know that tan ax 14 is 2.5 or five over two, 15 and that tan represents opposite over adjacent. 16 So this angle over our, 17 sorry, this side 20 over Y so now, 18 because we know that the opposite over adjacent is 20 over Y and that 19 the tan of angle X is five over two. 20 We can set those equal to each other and solve for Y. 21 So I'm going to cross multiply to get five. 22 Y is equal to 40, 23 and then I'm going to divide both sides by five to get Y is 24 equal to eight, and that's our.