A ramp forms a 30-degree angle with the ground. If the length of the ramp (hypotenuse) is 30 feet, the horizontal distance (adjacent side) from the base of the ramp to the wall isfeet.
Answer & Analysis
Analysis
Question Analysis
This problem evaluates the application of the cosine function in a real-world context, specifically in a 30-60-90 right triangle.
Key Concept Explanation
In a 30-60-90 triangle, the cosine of the 30-degree angle is . The cosine function relates the adjacent side to the hypotenuse.
Step-by-step Solution
1. Identify the given values: hypotenuse = 30 feet, angle = 30 degrees.
2. Use the cosine of 30 degrees:
3. Set up the equation:
4. Substitute the cosine value:
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