Triangle ABC is a right triangle, meaning we can use the Pythagorean Theorem to find x. The formula for the Pythagorean Theorem is: [tex]a = \sqrt{ {b}^{2} + {c}^{2} } [/tex] where a is the hypotenuse, and b and c are the legs. In this problem, we have the vertical leg as 16, the horizontal leg as x, and the hypotenuse as 20. Therefore, we can say that [tex]a = 20 \\ b = 16 \\ c = x[/tex] Therefore, we can plug into the formula to find x:[tex]a = \sqrt{ {b}^{2} + {x}^{2} } \\ {a}^{2} = { \sqrt{ {b}^{2} + {x}^{2} } }^{2} \\ {a}^{2} = {b}^{2} + {x}^{2} \\ {a}^{2} - {b}^{2} = {x}^{2}[/tex] We first change the variable c to x and square both sides of the equation. Then we subtract b^2 from both sides. [tex] {x}^{2} = {a}^{2} - {b}^{2} \\ \sqrt{ {x}^{2} } = \sqrt{ {a}^{2} - {b}^{2} } \\ x = \sqrt{ {a}^{2} - {b}^{2} } [/tex] We square root each side to find the variable answer for x. Then we plug in the numbers:[tex]x = \sqrt{ {(20)}^{2} - {(16)}^{2} } \\ x = \sqrt{400 - 256} \\ x = \sqrt{144} \\ x = 12[/tex] We find that x = 12. The answer is A. 12.
