Algebra-2

Question Analysis
This problem tests the application of the cosine function in a real-world context involving a 45-45-90 triangle.

Key Concept Explanation
In a 45-45-90 triangle, the sides are in the ratio $$ 1 : 1 : \sqrt{2} $$. The cosine of 45 degrees is $$ \frac{1}{\sqrt{2}} $$ or $$ \frac{\sqrt{2}}{2} $$.

Step-by-step Solution
1. Identify the given values: adjacent side (shadow) = 10 feet, angle = 45 degrees
2. Use the cosine of 45 degrees: $$ \cos(45^\circ) = \frac{1}{\sqrt{2}} $$
3. Set up the equation: $$ \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{10}{\text{hypotenuse}} = \...