What you’ll learn
Solve elevation/depression problems.
Key idea
Tangent relates vertical separation to horizontal run; the sloping sight line is not the run.
The angle is measured from horizontal; do not substitute sloped distance or invent an observer offset.
Worked example
Enter the exact value or ordered values in the format requested below.
A ground-level observer sees a vertical pole top at acute elevation theta, measured above horizontal. Horizontal run to the base is 15 m; tan(theta)=12/5. Find the pole height in meters.
- The height is opposite and horizontal run 15 is adjacent: height/15=12/5.
- Height=15*12/5=36 m.
Answer: 36
Quick Check
Evaluate a worked attempt at solve elevation/depression problems, identify the first invalid step, and provide the correction.
A ground-level observer has horizontal run 20 m to a pole and elevation theta with tan(theta)=21/20. Step 1 labels pole height adjacent to theta. Step 2 uses cosine with height over run. Locate the first invalid step and give the corrected height in meters.