SOLUTION: Right triangle ABC has a right angle at C and hypotenuse length 12. Angle A is pi/6 radians. Please sketch this triangle, including the measures of all angles in degrees and the le

Algebra ->  Triangles -> SOLUTION: Right triangle ABC has a right angle at C and hypotenuse length 12. Angle A is pi/6 radians. Please sketch this triangle, including the measures of all angles in degrees and the le      Log On


   

Question 1088317: Right triangle ABC has a right angle at C and hypotenuse length 12. Angle A is pi/6 radians. Please sketch this triangle, including the measures of all angles in degrees and the lengths of all sides. the lengths of all sides must be EXACT!
I have this so far c=12
pi/6 radians= pi/6(180/pi) = 30 degrees
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
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A%2BB%2BC=2pi
pi%2F6%2BB%2Bpi%2F2=pi
B=pi%281-1%2F6-1%2F2%29
B=pi%286%2F6-1%2F6-3%2F6%29
B=pi%282%2F6%29
B=pi%2F3
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Using the law of sines,
sin%28A%29%2Fa=sin%28B%29%2Fb=sin%28C%29%2Fc
So then,
sin%28pi%2F2%29%2F12=sin%28pi%2F6%29%2Fa
Solve for a.
sin%28pi%2F2%29%2F12=sin%28pi%2F3%29%2Fb
Solve for b.
Or use the Pythagorean theorem,
c%5E2=a%5E2%2Bb%5E2
b%5E2=144-a%5E2
b=sqrt%28144-a%5E2%29