Since this is a 30-60-90 right triangle, we know that the sides exist in the proportion 1:3‾√
:2. The shortest side, 1, is opposite the 30 degree angle. Since side X is opposite the 60 degree angle, we know that it is equal to 1∗3‾√
Or about 1.73. Finally, side Y is opposite the right angle, and it is twice the shortest side, or 2.
Let the two integers be x and y respectively
Hence;
![x + y = - 15 \\ \\ xy = 54](https://tex.z-dn.net/?f=x%20%2B%20y%20%3D%20%20-%2015%20%5C%5C%20%20%5C%5C%20xy%20%3D%2054)
From the first equation ;
![x = - 15- y](https://tex.z-dn.net/?f=x%20%3D%20%20-%2015-%20y)
Substitute into the third equation
![( - 15 - y)y = 54](https://tex.z-dn.net/?f=%28%20-%2015%20-%20y%29y%20%3D%2054)
Open up the bracket
![- 15y - {y}^{2} = 54](https://tex.z-dn.net/?f=%20-%2015y%20-%20%20%7By%7D%5E%7B2%7D%20%20%3D%2054)
Take everything to the right hand side of the equation and you'll have a quadratic equation
![0 = 54 + 15y + {y}^{2}](https://tex.z-dn.net/?f=0%20%3D%2054%20%2B%2015y%20%2B%20%20%7By%7D%5E%7B2%7D%20)
Solve the quadratic equation and you'll have two roots
![y= - 6 \: or \: y= -9](https://tex.z-dn.net/?f=y%3D%20%20-%206%20%5C%3A%20or%20%5C%3A%20y%3D%20-9)
Substitute for each value of y in the first equation
Therefore:
![x + ( - 6) = - 15 \: \\ or \\ \: x + ( - 9) = - 15](https://tex.z-dn.net/?f=x%20%20%2B%20%28%20-%206%29%20%3D%20%20-%2015%20%5C%3A%20%20%5C%5C%20or%20%5C%5C%20%20%5C%3A%20x%20%2B%20%28%20-%209%29%20%3D%20%20-%2015)
![x - 6 = - 15 \\ or \\ x - 9 = - 15](https://tex.z-dn.net/?f=x%20-%206%20%3D%20%20-%2015%20%5C%5C%20or%20%5C%5C%20x%20-%209%20%3D%20%20-%2015)
![x = - 15 + 6 \\ or \\ x = - 15 + 9](https://tex.z-dn.net/?f=x%20%3D%20%20-%2015%20%2B%206%20%5C%5C%20or%20%5C%5C%20x%20%3D%20%20-%2015%20%2B%209)
![x = - 9 \: or \: x = - 6](https://tex.z-dn.net/?f=x%20%3D%20%20-%209%20%5C%3A%20or%20%5C%3A%20x%20%3D%20%20-%206)
Therefore the answer is A
10 is the initial value, found when x=0. I don't know what you are measuring by "0" and "10" here, so can't be more specific.