Use the Pythagorean relationship
See this course’s project requirements
A desk-based right-triangle investigation with labeled sides, ratio choices, checked distances and an uncertainty comparison.
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What to include
- Label all three sides relative to a chosen angle.
- Check one Pythagorean calculation.
- Choose ratios from known and unknown sides.
- Show a distance and an inverse-angle calculation.
- Include observer offset, uncertainty and all changed cases in the height model.
Review and revise
Use these criteria to check your work and choose what to improve.
- Method: applies the course-specific rules to the supplied cases with visible intermediate work.
- Accuracy: results agree with the stated facts, units, boundaries and independent checks.
- Reasoning: explains why the result follows and identifies a limitation or unresolved question.
- Transfer: completes changed cases and revises the final project when a relevant assumption changes.
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The idea in everyday life
Case: right triangle legs 9 cm and 12 cm; missing hypotenuse c.
For a right triangle, a²+b²=c² with c the hypotenuse. Taking a square root converts a squared length back to length. The formula must not be applied to a triangle without a right-angle condition.
Use the Pythagorean relationship — worked practice
For a right triangle, a²+b²=c² with c the hypotenuse. Taking a square root converts a squared length back to length. The formula must not be applied to a triangle without a right-angle condition.
Case: right triangle legs 9 cm and 12 cm; missing hypotenuse c.
Case information
Paste at A1.
| ARecord | BGiven |
|---|---|
| Original case | Case: right triangle legs 9 cm and 12 cm; missing hypotenuse c. |
Copy as plain text
1. 1. Square
Square each leg.
You should see: 9²=81; 12²=144.
2. 2. Add
Calculate c².
You should see: c²=225cm².
3. 3. Root
Take the positive square root for length.
You should see: c=15 cm.
4. 4. Check
Compare size and substitute.
You should see: 15 exceeds both legs; 81+144=225.
What to finish
A squared-length calculation, positive square root and substitution check.
Watch for this
The diagonal relationship is c²=a²+b².
How can I tell I understand it?
Use squared values and a positive root without confusing a side sum with the diagonal.
Quick knowledge check
Answer all 3 questions. Get at least 2 right and the lesson completes automatically.
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Answer all 3 questions above and get at least 2 right. You can review the explanations and try again.
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