SAT Question 7700d098: Right Triangles And Trigonometry answer and explanation with Desmos solution

Choice C is correct. The Pythagorean theorem states that for a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. It's given that one leg of a right triangle has a length of $43.2$ millimeters. It's also given that the hypotenuse of the triangle has a length of $196.8$ millimeters. Let $b$ represent the length of the other leg of the triangle, in millimeters. Therefore, by the Pythagorean theorem, $43.2^2+b^2=196.8^2$, or $1,866.24+b^2=38,730.24$. Subtracting $1,866.24$ from both sides of this equation yields $b^2=36,864$. Taking the positive square root of both sides of this equation yields $b=192$. Therefore, the length of the other leg of the triangle, in millimeters, is $192$.