Triangle solver

<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>Known information</strong></th><th style="text-align: center; --cell-justify: center"><strong>Useful first step</strong></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">Two angles and one side</td><td style="text-align: center; --cell-justify: center">Find the third angle, then use the sine rule.</td></tr><tr><td style="text-align: center; --cell-justify: center">Two sides and their included angle</td><td style="text-align: center; --cell-justify: center">Use the cosine rule to find the third side.</td></tr><tr><td style="text-align: center; --cell-justify: center">Three sides</td><td style="text-align: center; --cell-justify: center">Use the cosine rule to find an angle.</td></tr><tr><td style="text-align: center; --cell-justify: center">Two sides and an angle opposite one of them</td><td style="text-align: center; --cell-justify: center">Use the sine rule, then check every possible angle.</td></tr></tbody></table></div></div>
<p>Cosine rule: \(a^2=b^2+c^2-2bc\cos A\). The angle \(A\) is between sides \(b\) and \(c\), and opposite side \(a\).</p>
<p>For three given sides, \(\cos A=\dfrac{b^2+c^2-a^2}{2bc}\). A negative value of \(\cos A\) gives an obtuse angle. The largest angle is opposite the longest side.</p>
<p>Keep the full calculator value for later steps. Round only each final answer to the accuracy requested; 3 significant figures is not the same as 3 decimal places.</p>

Cosine rule: \(a^2=b^2+c^2-2bc\cos A\). The angle \(A\) is between sides \(b\) and \(c\), and opposite side \(a\).

For three given sides, \(\cos A=\dfrac{b^2+c^2-a^2}{2bc}\). A negative value of \(\cos A\) gives an obtuse angle. The largest angle is opposite the longest side.

Keep the full calculator value for later steps. Round only each final answer to the accuracy requested; 3 significant figures is not the same as 3 decimal places.

Choosing a triangle rule

Choosing a triangle rule

Known information	Useful first step
Two angles and one side	Find the third angle, then use the sine rule.
Two sides and their included angle	Use the cosine rule to find the third side.
Three sides	Use the cosine rule to find an angle.
Two sides and an angle opposite one of them	Use the sine rule, then check every possible angle.