A ladder leaning against a wall makes a 45-degree angle with the ground. If the ladder is 20 feet long, the height at which it touches the wall isfeet.
Answer & Analysis
Analysis
Question Analysis
This problem assesses the application of the sine ratio in a real-world context, specifically in a 45-45-90 triangle.
Key Concept Explanation
In a 45-45-90 triangle, the sides are in the ratio 1:1: . The sine of 45 degrees is . The sine ratio can be used to find the length of the opposite side (height of the ladder).
Step-by-step Solution
1. Identify the given values: angle = 45 degrees, hypotenuse = 20 feet.
2. Use the sine ratio for 45 degrees:
3. Solve for the opposite side:
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