Math Problem Statement
Solution
To find the length of the third side of the right triangle, we can apply the Pythagorean Theorem, which is expressed as:
Where and are the two legs of the right triangle, and is the hypotenuse.
Given:
- The first leg is 7.
- The hypotenuse is 24.
We are looking for the second leg. Let’s denote it as .
Using the Pythagorean Theorem:
Simplifying:
Now, solve for :
Now, take the square root of both sides to find :
Calculating the square root:
Thus, the length of the third side is approximately 22.9 units, rounded to the nearest tenth.
Would you like a more detailed explanation, or do you have any other questions?
Here are some related questions for further exploration:
- What happens if you change one of the triangle's side lengths?
- How does the Pythagorean Theorem apply to non-right triangles?
- Can the Pythagorean Theorem be used in 3D geometry?
- How do trigonometric ratios relate to right triangles?
- What are the conditions for a triangle to be classified as a right triangle?
Tip: Always remember to double-check whether the triangle is a right triangle before using the Pythagorean Theorem.
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Math Problem Analysis
Mathematical Concepts
Geometry
Right Triangles
Pythagorean Theorem
Formulas
a^2 + b^2 = c^2
Theorems
Pythagorean Theorem
Suitable Grade Level
Grades 6-8
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