anonymous
  • anonymous
If you have a triangle with angles of 30, 60 and 90 with a side of 12, what would the other two sides be?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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amistre64
  • amistre64
which side is 12?
amistre64
  • amistre64
side opposite 30 = 12? side opposite 60 = 12? or side opposite 90 = 12? these are 3 different results....
anonymous
  • anonymous
oops I wrote it wrong, the side opposite is 21

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anonymous
  • anonymous
opposite 30
anonymous
  • anonymous
you can use the law of of sines or cosines to get the answer
anonymous
  • anonymous
law of sines is \[sineA/a=sinb/b\]
anonymous
  • anonymous
\[Sin 30/21=sine 60/x\]
anonymous
  • anonymous
cross multiply sin 30 x=(21)(sin60)
anonymous
  • anonymous
Use a calculator to figure out the sines .05x = (21)(0.86602540378444) x=9.09326673973662
anonymous
  • anonymous
so the side opposite 60 deg. is 9.09326673973662
amistre64
  • amistre64
if you can visualize the 30-60-90 triangle (or draw it); then things get simpler as well; the slanted part(hypotenuse) has a normal value = 2 the leg opp. 60 has a normal value = sqrt(3) the leg opp. 30 has a normal value = 1 since opp 30 = 21 in your problem, then 1x = 21..x = 21 we want to multiply all these "normal" values by 21 to get the measurements of the other 2 sides: slant = 2(21) = 42 and leg opp 60 = 21sqrt(3) or 36.37
anonymous
  • anonymous
I messed up in the last part of the algebra

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