A ladder leaning against a wall makes a 45-degree angle with the ground. If the ladder is 16 feet long, the height at which it touches the wall isfeet.
Answer & Analysis
Analysis
Question Analysis
This problem applies the sine ratio in a real-world context, specifically using the properties of a 45-45-90 triangle.
Key Concept Explanation
In a 45-45-90 triangle, the sides are in the ratio 1:1:√2. The sine of a 45-degree angle is always .
Step-by-step Solution
1. Identify the given values: ladder length (hypotenuse) = 16 feet, angle = 45 degrees.
2. Use the sine ratio:
3. Substitute the known sine value:
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