SOLUTION: In 30:60:90 triangles, if the side opposite the 30 is 5 units long, how long is the side opposite thev60?

Algebra ->  Proportions -> SOLUTION: In 30:60:90 triangles, if the side opposite the 30 is 5 units long, how long is the side opposite thev60?      Log On


   

Question 697889: In 30:60:90 triangles, if the side opposite the 30 is 5 units long, how long is the side opposite thev60?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The ratios if the sides opposite the are:
30: +1+
60: +sqrt%283%29+
90: +2+
------------
So, I can say:
( side opposite 30 ) / ( side opposite 60 ) = +1+%2F+sqrt%283%29+
Let +x+ = the length of the side opposite the 60 degree angle
given:
+5%2Fx+=+1%2Fsqrt%283%29+
+5%2Asqrt%283%29+=+x+
+x+=+1.732%2A5+
+x+=+8.66+
The length of the side opposite the 60 degree angle is 8.66 units long
Check answer:
+5%5E2+%2B+8.66%5E2+=+25+%2B+74.996+
+5%5E2+%2B+8.66%5E2+=+100+
The side opposite 90 is +sqrt%28100%29+=+10+ which is correct, since
+5%2F10+=+1%2F2+