A triangle has sides A, B, and C. The angle between sides A and B is (pi)/2π2. If side C has a length of 12 12 and the angle between sides B and C is pi/12π12, what is the length of side A?

1 Answer

The three sides are:

A=3sqrt2(sqrt3+1)A=32(3+1)

B=3sqrt2(sqrt3-1)B=32(31)

C=12C=12

Explanation:

C=12C=12

theta_C=pi/2θC=π2

theta_A=pi/12θA=π12

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

Adjacent side A=Ccostheta_AA=CcosθA

=12cos(pi/12)=12cos(π12)

cos(pi/12)=(sqrt(3)+1)/(2sqrt2)cos(π12)=3+122

A=12xx(sqrt(3)+1)/(2sqrt2)=3sqrt2(sqrt3+1)A=12×3+122=32(3+1)

B=Csin(pi/12)B=Csin(π12)

sin(pi/12)=(sqrt(3)-1)/(2sqrt2)sin(π12)=3122

A=12xx(sqrt(3)-1)/(2sqrt2)=3sqrt2(sqrt3-1)A=12×3122=32(31)

The three sides are:

A=3sqrt2(sqrt3+1)A=32(3+1)

B=3sqrt2(sqrt3-1)B=32(31)

C=12C=12