Math Problem Statement
If an airplane passes directly over your head at an altitude of 8 kilometers, how far is the airplane from your position after it has flown 15 kilometers farther at the same altitude?
Solution
To determine the airplane's distance from your position after flying 15 km at a constant altitude of 8 km, we can use the Pythagorean theorem.
Given:
- Initial altitude of the airplane: km
- Horizontal distance traveled: km
We treat this as a right triangle where:
- One leg is the altitude of the airplane ( km).
- The other leg is the horizontal distance it has traveled ( km).
- The hypotenuse () is the direct distance from the observer to the airplane.
Using the Pythagorean theorem:
Final Answer:
The airplane is 17 kilometers away from your position.
Would you like further explanation or a diagram?
Here are five related questions to expand on this concept:
- What is the distance from your position if the airplane traveled 20 km instead?
- How would the distance change if the airplane's altitude was 10 km instead of 8 km?
- If the airplane continued flying at the same altitude, at what horizontal distance would it be 25 km away from you?
- How would you calculate the angle of elevation from your position after the airplane has traveled 15 km?
- What if the airplane was descending at a constant rate while flying forward? How would the distance calculation change?
Tip: The Pythagorean theorem is essential for solving problems involving right triangles in real-world applications like navigation and physics.
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Math Problem Analysis
Mathematical Concepts
Geometry
Right Triangles
Distance Calculation
Formulas
Pythagorean Theorem: a^2 + b^2 = c^2
Theorems
Pythagorean Theorem
Suitable Grade Level
Grades 8-10