document.write( "Question 388987: THe ratio of the angles of a triangle is 1:2:3. If the shortest side of the triangle has length 5 square root of 3. what is the length of the next larger side? \n" ); document.write( "

Algebra.Com's Answer #275470 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"a+%2B+2a+%2B+3a+=+180\"$
\n" ); document.write( " $\"6a+=+180\"$
\n" ); document.write( " $\"a+=+30\"$
\n" ); document.write( " $\"2a+=+60\"$
\n" ); document.write( " $\"3a+=+90\"$
\n" ); document.write( "The shortest side is opposite the smallest angle
\n" ); document.write( "the ratios of the sides of a 30-60-90 triangle are
\n" ); document.write( " $\"1\"$ : $\"sqrt%283%29\"$ : $\"2\"$
\n" ); document.write( " $\"1%2Fsqrt%283%29+=+5%2Asqrt%283%29%2Fx\"$
\n" ); document.write( " $\"x+=+5%2Asqrt%283%29%2Asqrt%283%29\"$
\n" ); document.write( " $\"x+=+15\"$
\n" ); document.write( "The next longer side is 15 units long
\n" ); document.write( "check:
\n" ); document.write( "sides are:
\n" ); document.write( "opposite 30: $\"5%2Asqrt%283%29\"$
\n" ); document.write( "opposite 60: $\"15\"$
\n" ); document.write( "opposite 90: $\"10%2Asqrt%283%29\"$
\n" ); document.write( " $\"%285%2Asqrt%283%29%29%5E2+%2B+15%5E2+=+%2810%2Asqrt%283%29%29%5E2\"$
\n" ); document.write( " $\"75+%2B+225+=+300\"$
\n" ); document.write( " $\"300+=+300\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );