Question 697889
The ratios if the sides opposite the are:
30: {{{ 1 }}}
60: {{{ sqrt(3) }}}
90: {{{ 2 }}}
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So, I can say:
( side opposite 30 ) / ( side opposite 60 ) = {{{ 1 / sqrt(3) }}}
Let {{{ x }}} = the length of the side opposite the 60 degree angle
given:
{{{ 5/x = 1/sqrt(3) }}}
{{{ 5*sqrt(3) = x }}}
{{{ x = 1.732*5 }}}
{{{ x = 8.66 }}}
The length of the side opposite the 60 degree angle is 8.66 units long
Check answer:
{{{ 5^2 + 8.66^2 = 25 + 74.996 }}}
{{{ 5^2 + 8.66^2 = 100 }}}
The side opposite 90 is {{{ sqrt(100) = 10 }}} which is correct, since
{{{ 5/10 = 1/2 }}}