Triangle solver

<p>Two sides and a non-included angle can give no triangle, one triangle or two triangles. Do not assume that the principal inverse-sine answer is the only possibility.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="width: 100%;"><thead><tr><th style="text-align: center; --cell-justify: center"><strong>Check</strong></th><th style="text-align: center; --cell-justify: center"><strong>Consequence</strong></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">Calculated \(\sin B&gt;1\)</td><td style="text-align: center; --cell-justify: center">No triangle has this data.</td></tr><tr><td style="text-align: center; --cell-justify: center">Calculated \(\sin B=k\), with \(0&lt;k&lt;1\)</td><td style="text-align: center; --cell-justify: center">Check both&nbsp;\(B_1=\sin^{-1}(k)\) and \(B_2=180^\circ-B_1\).</td></tr><tr><td style="text-align: center; --cell-justify: center">For each candidate, \(A+B&lt;180^\circ\)</td><td style="text-align: center; --cell-justify: center">Only candidates leaving a positive third angle are valid.</td></tr></tbody></table></div></div>
<p>If&nbsp;\(\sin B=1\), then&nbsp;\(B=90^\circ\): the supplementary value is the same angle, not a second triangle. It still needs a positive third angle.</p>
<p>Check side-angle ordering as well: a longer side is opposite a larger angle. Report each valid triangle separately, and use unrounded angles for any subsequent side or area calculation.</p>

Two sides and a non-included angle can give no triangle, one triangle or two triangles. Do not assume that the principal inverse-sine answer is the only possibility.

If \(\sin B=1\), then \(B=90^\circ\): the supplementary value is the same angle, not a second triangle. It still needs a positive third angle.

Check side-angle ordering as well: a longer side is opposite a larger angle. Report each valid triangle separately, and use unrounded angles for any subsequent side or area calculation.

Check	Consequence
Calculated \(\sin B>1\)	No triangle has this data.
Calculated \(\sin B=k\), with \(0<k<1\)	Check both \(B_1=\sin^{-1}(k)\) and \(B_2=180^\circ-B_1\).
For each candidate, \(A+B<180^\circ\)	Only candidates leaving a positive third angle are valid.

Checking triangle solutions

Checking triangle solutions