SAT Question 6c67dd47: Right Triangles And Trigonometry answer and explanation with Desmos solution

Choice C is correct. The area, $A$, of a triangle is given by the formula $A=\frac{1}{2}bh$, where $b$ is the length of a base of the triangle and $h$ is its corresponding height. It’s given that the length of $\overline{XY}$ is $26$ units. This length represents a base of the triangle, so $b=26$. Let $h$ represent its corresponding height. It's given that the measure of angle $X$ is $54^{\circ }$ and the length of $\overline{XZ}$ is $19$ units. It follows that $\sin 54^{\circ }=\frac{h}{19}$. Multiplying both sides of this equation by $19$ yields $19\sin 54^{\circ }=h$. Substituting $26$ for $b$ and $19\sin 54^{\circ }$ for $h$ in the formula $A=\frac{1}{2}bh$ yields $A=\frac{1}{2}(26)(19\sin 54^{\circ })$, or $A=247\sin 54^{\circ }$. Therefore, the area, in square units, of triangle $XYZ$ is $247\sin 54^{\circ }$.