Choose sine, cosine or tangent
See this course’s project requirements
A desk-based right-triangle investigation with labeled sides, ratio choices, checked distances and an uncertainty comparison.
Keep your working files in your own notebook or software. Save a private description, checklist, and work link in My Proof.
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.
Want more background?
The idea in everyday life
Case: relative to θ, opposite 6, adjacent 8, hypotenuse 10 cm.
For an acute angle in a right triangle, sin=opposite/hypotenuse, cos=adjacent/hypotenuse, tan=opposite/adjacent. Select the ratio connecting the known quantity and the requested quantity, not whichever button is convenient.
Choose sine, cosine or tangent — worked practice
For an acute angle in a right triangle, sin=opposite/hypotenuse, cos=adjacent/hypotenuse, tan=opposite/adjacent. Select the ratio connecting the known quantity and the requested quantity, not whichever button is convenient.
Case: relative to θ, opposite 6, adjacent 8, hypotenuse 10 cm.
Case information
Paste at A1.
| ARecord | BGiven |
|---|---|
| Original case | Case: relative to θ, opposite 6, adjacent 8, hypotenuse 10 cm. |
Copy as plain text
1. 1. Sine
Divide opposite by hypotenuse.
You should see: sinθ=6/10=0.6.
2. 2. Cosine
Divide adjacent by hypotenuse.
You should see: cosθ=8/10=0.8.
3. 3. Tangent
Divide opposite by adjacent.
You should see: tanθ=6/8=0.75.
4. 4. Choose
Identify the ratio for opposite when adjacent and θ are known.
You should see: Tangent links those two legs.
What to finish
A sine/cosine/tangent ratio comparison with cancellation of length units.
Watch for this
Sine for an acute right-triangle angle is at most 1 because the opposite leg is shorter than the hypotenuse.
How can I tell I understand it?
Select a ratio based on the supplied side roles rather than a calculator button.
Quick knowledge check
Answer all 3 questions. Get at least 2 right and the lesson completes automatically.
You’ll get an explanation for each answer. Signed in? Your results save to your account.
Pass the check. We’ll save the progress.
Answer all 3 questions above and get at least 2 right. You can review the explanations and try again.
Go to the knowledge checkTools, templates, and lesson sources
Tools and templates
Tools open in a new tab so you can keep your place here.
Sources and further reading
Explore the references behind this lesson.
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.
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.
Report a problem with this lesson
Tell us what went wrong. Please leave out personal information and private project contents.