Math Problem Statement
A kite is flying 12 ft off the ground. Its line is pulled taut and casts a 9 ft shadow. Find the length of the line.
Solution
This problem involves using the Pythagorean Theorem to find the length of the kite's line. The scenario described forms a right triangle, with the height and the shadow as the two legs of the triangle, and the kite’s line as the hypotenuse.
- Height: 12 feet (vertical distance from the ground to the kite)
- Base: 9 feet (the length of the shadow)
- Hypotenuse: the kite's line, which we need to find.
The Pythagorean Theorem states:
where:
- (height),
- (shadow or base),
- is the length of the kite's line.
Substitute the values into the formula: Taking the square root of both sides:
Therefore, the length of the kite's line is 15 feet.
Would you like further clarification, or do you have any other questions?
Here are some related questions:
- How does the Pythagorean Theorem work in real-life applications?
- What other methods could be used to solve for the hypotenuse if the triangle was not a right triangle?
- How would the solution change if the height or shadow were different?
- Could trigonometry help solve this type of problem more efficiently?
- How can we apply similar techniques to problems involving three-dimensional geometry?
Tip: Always verify whether a triangle is a right triangle before applying the Pythagorean theorem.
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Math Problem Analysis
Mathematical Concepts
Geometry
Pythagorean Theorem
Formulas
a^2 + b^2 = c^2
Theorems
Pythagorean Theorem
Suitable Grade Level
Grades 7-9