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 $2$ and the angle between sides B and C is $( 5 pi)/12$ , what are the lengths of sides A and B?

Question

1551 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-04-22T15:16:14

side $a=sqrt(6)+sqrt(2)=3.863703305$
side $b=sqrt(6)+sqrt(2)=3.863703305$

The given parts of the triangle are
side $c=2$
Angle $A=(5pi)/12=75^@$
Angle $C=pi/6=30^@$

The third angle $B$ can be readily solved

$A+B+C=180^@$

$75^@+B+30^@=180^@$

$B=180-105^@=75^@$

Therefore we have an isosceles triangle with angles A and B equal.

solve side $a$ using Sine Law

$a/sin A=c/sin C$

$a=(c*sin A)/sin C=(2*sin 75^@)/(sin 30^@)=sqrt(6)+sqrt(2)$
by the definition of Isosceles triangle

$b=a=sqrt(6)+sqrt(2)$

We can check triangle using the Mollweide's Equation which involves all the 6 parts of the triangle

$(a-c)/b=sin (1/2(A-C))/(cos (1/2(B)))$

$(sqrt(6)+sqrt(2)-2)/(sqrt(6)+sqrt(2))=sin (1/2(75-30))/(cos (1/2(75)))$

$0.4823619098=0.4823619098$

This means all the 6 parts are correct.

God bless....I hope the explanation is useful.

A triangle has sides A, B, and C. The angle between sides A and B is (pi)/6(pi)/6. If side C has a length of 2 2 and the angle between sides B and C is ( 5 pi)/12( 5 pi)/12, what are the lengths of sides A and B?