<p>A triangle has angles of <img alt="$30^\circ$" height="13" src="https://latex.artofproblemsolving.com/9/1/9/919bf5d461970fc8d905d63704ef763c08594184.png" width="24" /> and <img alt="$45^\circ$" height="15" src="https://latex.artofproblemsolving.com/8/a/d/8adb649f063149ebc97d3ee58c4fd38d4c440846.png" width="28" />. If the side opposite the <img alt="$45^\circ$" height="15" src="https://latex.artofproblemsolving.com/8/a/d/8adb649f063149ebc97d3ee58c4fd38d4c440846.png" width="28" /> angle has length <img alt="$8$" height="14" src="https://latex.artofproblemsolving.com/8/4/5/8455f3b5cb3b4880b8c9d782a5c1f0334db819eb.png" width="11" />, then the side opposite the <img alt="$30^\circ$" height="13" src="https://latex.artofproblemsolving.com/9/1/9/919bf5d461970fc8d905d63704ef763c08594184.png" width="24" /> angle has length</p> <p><img alt="$\textbf{(A) }4\qquad \textbf{(B) }4\sqrt{2}\qquad \textbf{(C) }4\sqrt{3}\qquad \textbf{(D) }4\sqrt{6}\qquad \textbf{(E) }6$" height="21" src="https://latex.artofproblemsolving.com/e/4/4/e443cd726024694c977cb0edca1a5a712a941a20.png" width="425" /></p>

Question No: 467

A triangle has angles of $30^\circ$ and $45^\circ$ . If the side opposite the $45^\circ$ angle has length $8$ , then the side opposite the $30^\circ$ angle has length

$\textbf{(A) }4\qquad \textbf{(B) }4\sqrt{2}\qquad \textbf{(C) }4\sqrt{3}\qquad \textbf{(D) }4\sqrt{6}\qquad \textbf{(E) }6$

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Tags: Trigonometry

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