A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/2#. If side C has a length of #12 # and the angle between sides B and C is #pi/12#, what is the length of side A?

1 Answer
Shiva Prakash M V
Jun 6, 2018

The three sides are:

#A=3sqrt2(sqrt3+1)#

#B=3sqrt2(sqrt3-1)#

#C=12#

Explanation:

#C=12#

#theta_C=pi/2#

#theta_A=pi/12#

The triangle is a right angled triangle with C as hypotenuse,

Adjacent side #A=Ccostheta_A#

#=12cos(pi/12)#

#cos(pi/12)=(sqrt(3)+1)/(2sqrt2)#

#A=12xx(sqrt(3)+1)/(2sqrt2)=3sqrt2(sqrt3+1)#

#B=Csin(pi/12)#

#sin(pi/12)=(sqrt(3)-1)/(2sqrt2)#

#A=12xx(sqrt(3)-1)/(2sqrt2)=3sqrt2(sqrt3-1)#

The three sides are:

#A=3sqrt2(sqrt3+1)#

#B=3sqrt2(sqrt3-1)#

#C=12#

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