# 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

#### Explanation:

Angle between

# 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)#