Posted by jay on Wednesday, October 7, 2009 at 7:46pm.
First, draw your triangle so you can see what you're doing. The short side, 12, will be opposite the small angle, 30.
We know that the sin of an angle = opposite over hypotenuse. The angle is 30, and we can look up sin(30)=0.5.
So opposite (which we know is 12) over hypotenuse = 1/2.
12/hypotenuse = 1/2
hypotenuse = 24.
Now we can get the final, adjacent, side in either of two ways:
1. Pythagoras: 12^2 + adjacent^2 = 24^2
or
2. use the definition of cos = adjacent over hypotenuse. We can look up cos(30) = sqrt(3)/2 or .8660. So:
adjacent/24 = .8660
and mutiply across from there.
The sides of the 30-60-90 triangel are in the ratio of 1:√3:2
your triangle is 12:a:b
so 1/12 = √3/a
a = 12√3
and 1/12 = 2/b
b = 24
the other two sides are 12√3 and 24
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