1. The problem involves a right triangle with a right angle at vertex Z, a side adjacent to the 41° angle measuring 22 units, and we want to find the length of side XY opposite the 41° angle. 2. To solve for the length of side XY, we use trigonometric ratios. The cosine of an angle in a right triangle is defined as the ratio of the adjacent side to the hypotenuse: $$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$ Similarly, the sine of an angle is the ratio of the opposite side to the hypotenuse: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ 3. Here, the side of length 22 is adjacent to the 41° angle, and XY is the hypotenuse. Using cosine: $$\cos(41^\circ) = \frac{22}{XY}$$ 4. To solve for XY, multiply both sides by XY and then divide both sides by $\cos(41^\circ)$: $$XY \cos(41^\circ) = 22$$ $$XY = \frac{22}{\cos(41^\circ)}$$ 5. Therefore, the equation to solve for XY is: $$XY = \frac{22}{\cos(41^\circ)}$$ This matches the third option given. "slug": "triangle side", "subject": "trigonometry", "desmos": {"latex": "y=\frac{22}{\cos(41^\circ)}","features": {"intercepts": true,"extrema": true}}, "q_count": 1