Explanation for Question 31 From the Math (Calc) Section on the 2017 May Sat
Question 31 is a first free response question. 2 And it says the solid lines in the figure above represents the root of 3 a football player. And the dash line represents the distance from his starting point 4 to the point at which the player was stopped. 5 What is the value of X? So if we look at our figure, 6 the route that the football player makes is a triangle and 7 this right here, that they draw right there tells us that we have a 8 right triangle. So to find the last side, 9 we can use Pythagoras theorem. So whenever we have a right triangle, 10 we know two of the three sides we can use the formula, 11 a squared plus B squared equals C squared. 12 And we doesn't matter what you labeled them. 13 The only important part is that C is always the high partners. 14 So in this case, C is 13. 15 I'm going to say eight is 12. 16 So we have, we just plug in. Now we have 12 squared 17 plus B squared equals 13 squared, 18 and it's a calculator section. So you can use your calculator if you need 19 to. We have 1 44 plus 20 B squared equals 1 69. 21 And now we just want to combine like terms since we're solving for B, 22 we want to put all the numbers on the right side. 23 So we subtract 1 44 from both sides like 24 that. And then we again can use our tracker later, 25 if you want to. Um, 26 we get B squared equals 25. 27 We're looking for a B, so to solve for B, 28 I'm going to move it over here to have a little bit more space. 29 We're looking for B take the square root of the left side. 30 So we also take the square to the right side, 31 which gives us B equals five. 32 And it's for your response to that's your final answer.