SAT Question de9148c4: Right Triangles And Trigonometry answer and explanation with Desmos solution

Choice C is correct. The Pythagorean theorem states that for a right triangle, $a^2+b^2=c^2$, where $a$ and $b$ represent the lengths of the legs and $c$ represents the length of the hypotenuse. It’s given that the right triangle shown has legs with lengths $12$ and $3$ and a hypotenuse with length $c$. Substituting $12$ for $a$ and $3$ for $b$ in the formula $a^2+b^2=c^2$ yields $12^2+3^2=c^2$.