|
Tangent:
error in angle
Finds (via Monte Carlo) the error in an angle from its tangent. |
|
|
| Height, h:
μ, δ |
|
Height of right-angled triangle
("opposite" leg). |
| Base, b:
μ, δ |
|
Base of right-angled triangle ("adjacent" leg). • |
| Pr(μ ± δ) |
% (2σ: 95.45 %,
3σ: 99.73 %) |
Assigned probability for interval. • |
| Graph |
|
Graph: independent var.s (h, b),
angle (β). • |
| N, .seed |
(M, million) |
No. of trials, random seed. • |
| tol, klass, ymax |
['0' (¬ '.0'), auto.] |
Tolerance, no. of histo. classes,
max. y for graph. • |
| Show values |
|
Shows the coordinates of the graph. • |
Finds the value and error of
the angle, β, in a right-angled triangle, such that
tan β = h ⁄ b,
from the measurement of its height, h
—the leg (or cathetus) opposite to the angle—
and its base, b —the leg adjacent to the angle—,
hence, β = arctan(h ⁄ b).
The method is Monte Carlo simulation. The
theoretical result.pdf,
also given, is: δβ = (sinβ)(cosβ)
√[ε²(h) + ε²(b)].
Thus, the theoretical and simulated results can be compared.
(The tolerance is for the numerical inversion of
the Gaussian distribution.)
Graphs are shown for the behaviour of:
the independent (Gaussian) variables (h and b); or
the dependent variable (β).
Note that the distribution of β is not Gaussian
(though possibly approximately so). |
| References: |
Plate: ErrorTangentAngle |
• Taylor, 1997 (see Bibliography), or Nepf (already cited).
• 1623-09-11: Angeli, Stefano degli, or 21.st of Sep.
(1697-10-11). |
