A triangle has sides A, B, and C. The angle between sides A and B is (pi)/6. If side C has a length of 1 and the angle between sides B and C is (7pi)/12, what are the lengths of sides A and B?
2 Answers
Apr 23, 2017
Explanation:
Angle between
Apr 23, 2017
a=(sqrt(2)+sqrt(6))/2
b=sqrt(2)
Explanation:
We can use the sine rule:
![]()
a/sinA=b/sinB=c/sinC
So we have:
A = (7pi)/12; C=pi/6; c==1
To find
a/sinA=c/sinC => a/sin((7pi)/12)=1/sin(pi/6)
:. a=sin((7pi)/12)/sin(pi/6) = (sqrt(2)+sqrt(6))/2
To find
A+B+C=pi=>B=pi-(7pi)/12-pi/6=pi/4
And as before applying thee sin rule gives:
b/sinB=c/sinC => b/sin(pi/4)=1/sin(pi/6)
:. b=sin(pi/4)/sin(pi/6) =sqrt(2)