Math Problem Statement
The angle of elevation to the top of a Building in New York is found to be 5 degrees from the ground at a distance of 1 mile from the base of the building. Using this information, find the height of the building. Round to two decimal places. Hint: 1 mile = 5280 feet
Solution
We can solve this problem using trigonometry, specifically the tangent function in a right triangle.
Step 1: Identify the Given Information
- The distance from the observer to the base of the building (adjacent side) = 1 mile = 5280 feet
- The angle of elevation (θ) = 5°
- The height of the building (opposite side) = ?
Using the tangent function, we have:
Step 2: Solve for
Rearrange the equation:
Using a calculator:
Final Answer:
The height of the building is 461.07 feet.
Do you need further clarification or details?
Related Questions:
- What would be the height if the angle of elevation was 10 degrees?
- How does the height change if the observer moves closer to the building?
- What is the distance needed for an angle of elevation of 15 degrees to the same height?
- How would the calculation change if the building was on an inclined plane?
- How do we measure the angle of elevation accurately in real-world applications?
Tip:
When using trigonometric functions, always ensure your calculator is in degree mode (not radians) unless specified otherwise.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Tangent Function
Right Triangles
Formulas
tan(θ) = opposite / adjacent
Theorems
Trigonometric Ratios
Suitable Grade Level
Grades 9-12
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