Math Problem Statement
Solution
The image shows a right triangle where the pond's width across is represented by , the unknown value we need to find. The triangle has two legs of lengths 150 feet and 250 feet.
This is a typical application of the Pythagorean Theorem, which states:
Where:
- and are the legs of the right triangle.
- is the hypotenuse (in this case, ).
Here, one leg is 150 feet, and the other leg is 250 feet, so we can apply the formula as:
Now, let's calculate it step by step:
So, the distance across the pond is approximately 291.5 feet, rounded to the nearest tenth.
Would you like further details or clarifications?
Here are 5 related questions to consider:
- How does the Pythagorean theorem apply to real-world problems?
- Can we generalize the Pythagorean theorem for non-right triangles?
- How would the solution change if the pond's shape was different, requiring different methods?
- What are some practical applications of the Pythagorean theorem in fields like construction or navigation?
- How can trigonometry be used to find missing sides in triangles not involving the Pythagorean theorem?
Tip: When solving right triangle problems, always ensure you correctly identify the hypotenuse as it is the longest side opposite the right angle.
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Math Problem Analysis
Mathematical Concepts
Geometry
Right Triangles
Pythagorean Theorem
Formulas
Pythagorean Theorem: a^2 + b^2 = c^2
Theorems
Pythagorean Theorem
Suitable Grade Level
Grades 8-10
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