TRI_SSA

This function solves side-side-angle (SSA) triangle inputs, where two sides and one non-included angle are known.

SSA can be ambiguous because the sine relationship may admit two valid angle solutions:

\sin(E) = \frac{e\sin(D)}{d}

Depending on geometry, there can be zero, one, or two triangles. The ssa_flag parameter chooses how to resolve ambiguous two-solution cases.

Excel Usage

=TRI_SSA(d, e, D, ssa_flag)

d (float, required): Known side opposite angle D (length units).
e (float, required): Second known side (length units).
D (float, required): Known non-included angle opposite side d (radians).
ssa_flag (str, optional, default: “forbid”): SSA ambiguity handling mode.

Returns (list[list]): A 2D array where the first row is [d, e, f] and the second row is [D, E, F].

Example 1: Solve SSA using acute branch selection

Inputs:

d	e	D	ssa_flag
8	10	0.6	acute

Excel formula:

=TRI_SSA(8, 10, 0.6, "acute")

Expected output:

Result
8	10	13.9206
0.6	0.783556	1.75804

Example 2: Solve SSA using obtuse branch selection

Inputs:

d	e	D	ssa_flag
8	10	0.6	obtuse

Excel formula:

=TRI_SSA(8, 10, 0.6, "obtuse")

Expected output:

Result
8	10	2.58609
0.6	2.35804	0.183556

Example 3: Solve SSA case with effectively unique geometry

Inputs:

d	e	D	ssa_flag
9	6	0.8	acute

Excel formula:

=TRI_SSA(9, 6, 0.8, "acute")

Expected output:

Result
9	6	12.0843
0.8	0.498647	1.84295

Example 4: Solve SSA with small known angle

Inputs:

d	e	D	ssa_flag
9	11	0.5	acute

Excel formula:

=TRI_SSA(9, 11, 0.5, "acute")

Expected output:

Result
9	11	16.9464
0.5	0.62607	2.01552

Python Code

external_packages = ['trianglesolver==1.2']

from trianglesolver import ssa as trianglesolver_ssa

def tri_ssa(d, e, D, ssa_flag='forbid'):
    """
    Solve a triangle from two sides and a non-included angle using SSA branch selection.

    See: https://pypi.org/project/trianglesolver/

    This example function is provided as-is without any representation of accuracy.

    Args:
        d (float): Known side opposite angle D (length units).
        e (float): Second known side (length units).
        D (float): Known non-included angle opposite side d (radians).
        ssa_flag (str, optional): SSA ambiguity handling mode. Valid options: Forbid, Acute, Obtuse. Default is 'forbid'.

    Returns:
        list[list]: A 2D array where the first row is [d, e, f] and the second row is [D, E, F].
    """
    try:
        result = trianglesolver_ssa(d, e, D, ssa_flag)
        return [[result[0], result[1], result[2]], [result[3], result[4], result[5]]]
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

d *

Known side opposite angle D (length units).

e *

Second known side (length units).

D *

Known non-included angle opposite side d (radians).

ssa_flag

SSA ambiguity handling mode.