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<title>Solving ASA Triangles</title>
<meta name="description" content="ASA means Angle, Side, Angle, it is when we know two angles and a side between the angles. To solve an ASA Triangle ..." />
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<h1 align="center">Solving ASA Triangles</h1>
<p align="center"><i>&quot;ASA&quot; means &quot;Angle, Side, Angle&quot;</i></p>
<table width="85%" border="0" align="center">
<tr>
<td><img src="images/triangle-asa.svg" alt="ASA Triangle" /></td>
<td>
<p>&quot;<i>ASA</i>&quot; is when we know two angles and a side <b>between</b> the angles.</p>
</td>
</tr>
</table>
<p>&nbsp;</p>
<table width="80%" border="0" align="center">
<tr>
<td>
<p>To solve an ASA Triangle</p>
<ul>
<li>find the third angle using <a href="../proof180deg.html">the three angles add to 180&deg;</a></li>
<li>then use <a href="trig-sine-law.html">The Law of Sines</a> to find each of the other two sides. </li>
</ul>
</td>
</tr>
</table>
<p>&nbsp;</p>
<div class="example">
<h3>Example 1</h3>
<p> <img src="images/trig-asaex1.gif" width="175" height="125" alt="trig ASA example" /></p>
<p>In this triangle we know:</p>
<ul>
<li>angle A = 76&deg;</li>
<li>angle B = 34&deg;</li>
<li>and c = 9 </li>
</ul>
<p>&nbsp;</p>
<p>It's easy to find angle <b>C</b> by using 'angles of a triangle add to 180&deg;':</p>
<p align="center">So C = 180&deg; &minus; 76&deg; &minus; 34&deg; = <b>70&deg;</b></p>
<p align="center">&nbsp;</p>
<p>We can now find side <b>a</b> by using The Law of Sines:</p>
<p align="center">a/sinA = c/sin C</p>
<p align="center">a/sin76&deg; = 9/sin70&deg;</p>
<p align="center"> a = (9/sin70&deg;) &times; sin76&deg;
<br> a = <b>9.29</b> to 2 decimal places</p>
<p>&nbsp;</p>
<p>Similarly we can find side <b>b</b> by using The Law of Sines:</p>
<p align="center">b/sinB = c/sin C</p>
<p align="center"> b/sin34&deg; = 9/sin70&deg;</p>
<p align="center"> b = (9/sin70&deg;) &times; sin34&deg;
<br> b = <b>5.36</b> to 2 decimal places</p>
<p>&nbsp;</p>
<p>Now we have completely solved the triangle i.e. we have found all its angles and sides. </p>
</div>
<p>&nbsp;</p>
<div class="example">
<h3>Example 2</h3>
<p> <img src="images/trig-asaex2.gif" width="199" height="130" alt="trig ASA example" /></p>
<p>This is also an ASA triangle.</p>
<p>First find angle <b>X</b> by using 'angles of a triangle add to 180&deg;':</p>
<p align="center">X = 180&deg; &minus; 87&deg; &minus; 42&deg; = <b>51&deg;</b></p>
<p>Now find side <b>y</b> by using The Law of Sines:</p>
<p align="center">y/sinY = x/sin X</p>
<p align="center"> y/sin(87&deg;) = 18.9/sin(51&deg;)</p>
<p align="center"> y = (18.9/sin(51&deg;)) &times; sin(87&deg;)
<br> y = <b>24.29</b> to 2 decimal places.</p>
<p>Similarly we can find <b>z</b> by using The Law of Sines:</p>
<p align="center">z/sinZ = x/sin X</p>
<p align="center">z/sin(42&deg;) = 18.9/sin(51&deg;)</p>
<p align="center">z = (18.9/sin(51&deg;)) &times; sin(42&deg;)
<br> z = <b>16.27</b> to 2 decimal places.</p>
</div>
<p>&nbsp;</p>
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<div class="related"> <a href="trig-solving-practice.html">Triangle Solving Practice</a> <a href="trig-sine-law.html">The Law of Sines</a> <a href="trig-cosine-law.html">The Law of Cosines</a> <a href="trig-solving-triangles.html">Solving Triangles</a> <a href="trigonometry-index.html">Trigonometry Index</a> <a href="index.html">Algebra Index</a> </div>
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