30-60-90 Triangles

<p><a href="https://www.prepswift.com/quizzes/quiz/prepswift-30-60-90-triangles" target="_blank">30-60-90 Triangles Exercise</a></p><p>In higher level mathematics, if we know two angles of a triangle and one of the sides, we can calculate the two missing sides. The good news is we don&#39;t have to worry about that on the GRE. However, we do have to memorize two specific cases. The <strong><u>first</u></strong> is below:</p> <p><strong><span style="color:#8e44ad;">$30$-$60$-$90$ Triangles</span></strong></p> <center><svg height="270.3928527832031" style=" width:661.8285522460938px; height:270.3928527832031px; background: #FFF; fill: none; " width="661.8285522460938" x="0" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" y="0"> <svg class="role-diagram-draw-area" xmlns="http://www.w3.org/2000/svg"><g class="shapes-region" style="stroke: black; fill: none;"><g class="composite-shape"><path class="real" d=" M186,9.4 L480.6,219.4 L186,219.4 Z" style="stroke-width: 1; stroke: rgb(0, 0, 0); fill: none; fill-opacity: 1;"></path></g><g class="composite-shape"><path class="real" d=" M186,202.4 L203,202.4 L203,219.4" style="stroke-width: 1; stroke: rgb(0, 0, 0); fill: none; fill-opacity: 1;"></path></g><g class="arrow-line"><path class="connection real" d=" M306.6,224.07 L318.6,224.07" stroke-dasharray="" style="stroke: rgb(0, 0, 0); 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We can still calculate the other two sides.</p> <p>For example, if the side length opposite the $60$&deg; side is $5$, the shortest side is $\frac{5}{\sqrt{3}}$ (<span style="color:#e74c3c;">notice we divided by $\sqrt{3}$ here</span>) and the hypotenuse is&nbsp;$2 \times \frac{5}{\sqrt{3}} = 10\sqrt{3}$</p>