Math Problem Statement
Solution
The question asks you to use the Pythagorean theorem to calculate the length of , given the triangle has a right angle, and two sides are and . Let’s solve this step-by-step.
Pythagorean Theorem
Where is the hypotenuse (the longest side, opposite the right angle), and and are the other two sides.
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Identify sides:
- Hypotenuse ():
- One leg ():
- Unknown ():
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Rearrange the formula to find :
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Substitute values:
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Solve for :
Final Answer
The length of is approximately 16.2 cm (to 1 decimal place).
Would you like me to go over this in more detail or clarify anything?
Here are 5 related questions to expand on this:
- How would the Pythagorean theorem apply if the triangle had sides given in different units (e.g., meters instead of centimeters)?
- What are some real-world applications of the Pythagorean theorem in construction or navigation?
- Can the Pythagorean theorem be used in non-right triangles? Why or why not?
- What is the difference between a perfect square and the square root when solving for unknowns?
- How can you verify the accuracy of your calculation when using square roots?
Tip: Always double-check whether the given side is the hypotenuse when applying the Pythagorean theorem—it’s a common mistake to mix up the sides!
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Math Problem Analysis
Mathematical Concepts
Geometry
Right Triangle
Pythagoras' Theorem
Formulas
c^2 = a^2 + b^2
b^2 = c^2 - a^2
Theorems
Pythagoras' Theorem
Suitable Grade Level
Grades 8-10