# Wndsn Elevation Calculator

High-precision elevation calculator. Companion to Wndsn Quadrant Telemeters: Low tech, high utility graphical distance computers from the Wndsn applied science lab.

Measuring ground distance and vantage point height from an elevation (or depression). ## Input

Determine `a, b, c` (use any unit (m, inch, ft, etc.) for size `s` at angular size `α`):

## Results

• Size of the object observed: `s = 14.4` m
• Elevation of observer: `a = 86.21` m
• Ground distance: `b = 62.87` m
• Sight distance: `c = 106.7` m

The display precision set is `.2`. To change that, edit the variable `&digits=x` in the URL where `0 <= x <= 9`.

## Explanation

When measuring -- with the Telemeter -- heights of objects that are not on the same level as the vantage point, the triangle becomes skewed and the resulting angular size is distorted if we are looking to solve right triangles. But we don't have to; thanks to the law of sines.

The same concept can be applied to measuring the distance to "skewed" objects without a right angle solution. Measure altitude difference relative to shared base, e.g. the distance to a lighthouse of known height, measured from a skyscraper of unknown height, or the altitude of a structure on a mountain, measured from a valley, or the distance and altitude of an airplane of known size.

[Load sample values (JSON) (XML) (CSV).]

1. Object of known height `s` = 14.4 m; `a, b, c` are unknown.
2. Measure `γ` from vertical to top of object (41.2°).
3. Measure `β` from vertical to base of object (36.1°).
4. Subtract `β` from `γ` for `α` (= 5.1°).
5. Determine the angle `θ` = 180° – `γ` (= 138.8°).
6. Following the law of sines;
`c / sin(θ) = s / sin(α)`
we calculate
`c = (s × sin(θ)) / sin(α)`
for a distance of the line of sight of:
`c` = 106.7 m
7. Switching triangles, we can now calculate the elevation `a` of our vantage point with;
`a = c × cos(β)`
a = 106.7 × 0.81
`a` = 86.21 m
8. Calculate ground distance `b` with;
`b = c × sin(β)`
b = 106.7 × 0.59
`b` = 62.87 m