1. Problem: Find the missing side length $x$ in the right triangle with legs $16\sqrt{3}$ and $16$, and hypotenuse $x$. 2. Formula: Use the Pythagorean theorem for right triangles: $$x^2 = a^2 + b^2$$ where $a$ and $b$ are the legs. 3. Calculation: $$x^2 = (16\sqrt{3})^2 + 16^2 = 16^2 \times 3 + 16^2 = 256 \times 3 + 256 = 768 + 256 = 1024$$ 4. Simplify: $$x = \sqrt{1024} = 32$$ 5. Answer: The missing side length $x$ is $32$. This corresponds to problem 1 with answer $4\sqrt{3}$ (pink) but the calculation shows $32$, so let's check the problem carefully. Since the problem states legs $16\sqrt{3}$ and $16$, hypotenuse $x$, the calculation is correct and $x=32$. Since the user asked for the first problem only, here is the solution for problem 1. "slug": "missing side", "subject": "geometry", "desmos": {"latex": "y=0","features": {"intercepts": true,"extrema": true}}, "q_count": 12