Check a height estimate and its limits
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
Supplied desk case: horizontal distance 12m, angle 45°, eye-level height 1.5m. Supplied tan 45°=1. Compare a distance estimate 11–13m.
A right-triangle height model requires a horizontal distance and an angle above the horizontal. Add the observer height if the vertical estimate starts at eye level. Measurement uncertainty and model assumptions matter; no climbing or roadside fieldwork is required.
Check a height estimate and its limits — worked practice
A right-triangle height model requires a horizontal distance and an angle above the horizontal. Add the observer height if the vertical estimate starts at eye level. Measurement uncertainty and model assumptions matter; no climbing or roadside fieldwork is required.
Supplied desk case: horizontal distance 12m, angle 45°, eye-level height 1.5m. Supplied tan 45°=1. Compare a distance estimate 11–13m.
Case information
Paste at A1.
| ARecord | BGiven |
|---|---|
| Original case | Supplied desk case: horizontal distance 12m, angle 45°, eye-level height 1.5m. Supplied tan 45°=1. Compare a distance estimate 11–13m. |
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1. 1. Model
Write height above the eye level.
You should see: h=12×tan 45°=12m.
2. 2. Add offset
Include the supplied eye-level height.
You should see: Total height 13.5m.
3. 3. Compare uncertainty
Use horizontal distances 11 and 13 with the same angle.
You should see: Total range 12.5–14.5m.
4. 4. Assemble
State assumptions and a bounded estimate.
You should see: Assumes level ground and the same vertical plane; 13.5m is a model estimate, not an exact survey.
What to finish
A total-height estimate, distance sensitivity range and model assumptions.
Watch for this
A calculation can be correct under imperfect measured or assumed inputs.
How can I tell I understand it?
Calculate a changed height case without presenting the desk model as an exact survey.
Quick knowledge check
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