Triangle geometry connects side lengths, angles, centers, and special lines inside one three-sided figure.
Use it to identify which side, angle, center, or theorem relationship the entered measurements support.
The relationship
Write the rule before calculating
Apply the selected inverse function on its stated principal real branch.
See the structure
What the calculation is doing
oppositeθhypotenuseApply the selected inverse function on its stated principal real branch.
Worked interpretation
Read the result in context
arcsin(0.5) = 30° = π/6.
Interpret with care
Important boundary
A triangle must satisfy its inequality and its known measurements may allow no solution, one solution, or an ambiguous pair of solutions.
Use the Mathematics collection to move between connected concepts without duplicating the calculation.
Extended domain
Principal complex inverse trigonometry
Inverse trig functions use their principal complex branches, making values outside the real domains meaningful.
Try an example
COMPLEX RESULT1.57079632679 − 1.31695789692i
Principal branch
Quick guide
How to use this calculator
Enter the known values and choose degrees or radians where the page offers a unit selector.
Select the intended function, identity family, or solve direction when needed.
Read the primary answer first, then inspect domain notes, supporting values, or the graph.
Calculation method
Apply the selected trigonometric relationship
Apply the selected inverse function on its stated principal real branch.
The calculator validates real-function domains and reports undefined angles or impossible triangles explicitly instead of displaying NaN, Infinity, or a misleading zero.
Worked example
Worked example
arcsin(0.5) = 30° = π/6.
Apply the selected inverse function on its stated principal real branch.
Supported inputs
Precision and limits
Angle units
Degree/radian selectors apply only to fields labelled as angles. Triangle-law angles are explicitly entered and returned in degrees. Sinusoidal model arguments are explicitly radians.
Numerical precision
Calculations use finite double-precision arithmetic and normally display 12 significant digits. Exact-value pages return symbolic radical forms only for their stated standard-angle table.
Supported magnitude
Numeric inputs may be zero or have absolute magnitude from 1e-100 through 1e100. This bounded range prevents floating-point underflow and overflow from being shown as meaningful results.
Domains and branches
The primary panel preserves the familiar real-angle workflow. The extended panel evaluates principal complex branches in radians and plots the result; reciprocal singularities still return an explicit error.
Calculator-specific rule
Results use principal real branches. Other cotangent conventions exist; this calculator uses arccot values from 0 through π.
