1. **State the problem:** We are given triangle WXY with angles $m\angle WXY = 45^\circ$, $m\angle YWX = 90^\circ$, and side $WX = 5$ feet. We need to determine which triangle (a), (b), or (c) is correct based on these conditions. 2. **Recall triangle angle sum rule:** The sum of interior angles in any triangle is $180^\circ$. Given $m\angle YWX = 90^\circ$ and $m\angle WXY = 45^\circ$, we can find the third angle $m\angle XYW$: $$m\angle XYW = 180^\circ - 90^\circ - 45^\circ = 45^\circ$$ 3. **Identify triangle type:** Since two angles are $45^\circ$ and one is $90^\circ$, triangle WXY is a right isosceles triangle with the right angle at $W$ and the other two angles equal. 4. **Use side length to find other sides:** In a right isosceles triangle, the legs adjacent to the right angle are equal. Given $WX = 5$ feet, then $WY = 5$ feet. 5. **Calculate hypotenuse $XY$ using Pythagorean theorem:** $$XY = \sqrt{WX^2 + WY^2} = \sqrt{5^2 + 5^2} = \sqrt{25 + 25} = \sqrt{50} = 5\sqrt{2} \approx 7.07$$ 6. **Compare with given triangles:** Triangle (a) is the smallest, (b) is bigger, and (c) is biggest. Since the hypotenuse is about 7.07 feet, the triangle with side lengths matching this is the correct one. 7. **Conclusion:** Triangle (b) matches the side lengths and angles correctly. 8. **Why only one triangle can be formed:** Given one right angle, one other angle, and one side adjacent to the right angle, the triangle is uniquely determined by the ASA (Angle-Side-Angle) postulate. No other triangle can have the same two angles and included side but different shape.