Calculate an unknown distance
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 with θ=30°, adjacent side 10 cm. Supplied tan 30°≈0.57735. Unknown opposite h.
A trigonometric equation connects a known angle and side to an unknown side. Work in degrees when the angle is in degrees. A supplied ratio value can be used without requiring a particular calculator interface.
Calculate an unknown distance — worked practice
A trigonometric equation connects a known angle and side to an unknown side. Work in degrees when the angle is in degrees. A supplied ratio value can be used without requiring a particular calculator interface.
Case: right triangle with θ=30°, adjacent side 10 cm. Supplied tan 30°≈0.57735. Unknown opposite h.
Case information
Paste at A1.
| ARecord | BGiven |
|---|---|
| Original case | Case: right triangle with θ=30°, adjacent side 10 cm. Supplied tan 30°≈0.57735. Unknown opposite h. |
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1. 1. Select
Choose the ratio using the adjacent and opposite legs.
You should see: tan 30°=h/10.
2. 2. Rearrange
Multiply by 10.
You should see: h=10×tan 30°.
3. 3. Calculate
Use the supplied ratio and round to two decimals.
You should see: h≈5.77 cm.
4. 4. Check
Explain why h is smaller than the adjacent leg.
You should see: 30° is less than 45°; tan 30°<1.
What to finish
A rearranged tangent equation with a rounded distance and angle-unit note.
Watch for this
Division would solve a different arrangement of known and unknown sides.
How can I tell I understand it?
Solve the changed distance case with the supplied degree-based ratio.
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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Source & access notes · checked 2026-10-01
Web open/search showed the official page, its topic heading and relevant concept description. This is a content/source check, not a provider endorsement. Exact topic chapters were opened in web result turn 325view 0–14.
Access: Official page retrieved with the web reader on 2026-10-01; interactive tools and videos were not certified by retrieval.
Reuse: Original fictional teaching cases, calculations, questions and examples; link and short factual paraphrase only. No copied source exercises or illustrations.
Source & access notes · checked 2026-10-01
Web open/search showed the official page, its topic heading and relevant concept description. This is a content/source check, not a provider endorsement.
Access: Official page retrieved with the web reader on 2026-10-01; interactive tools and videos were not certified by retrieval.
Reuse: Original fictional teaching cases, calculations, questions and examples; link and short factual paraphrase only. No copied source exercises or illustrations.
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