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 $3$ and the angle between sides B and C is $pi/12$ , what is the length of side A?

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Answer 1 · 2017-10-14T16:50:06

$A=3/2(sqrt6-sqrt2)~=1.55$

The Euler theorem (or sine theorem) states that:

$A/sin hat(BC)=B/sin hat(AC)=C/sin hat(AB)$

Let's find A by using the relation:

$A/sin hat(BC)=C/sin hat(AB)$

from which:

$A=(C*sin hat(BC))/sin hat(AB)=(3*sin(pi/12))/sin (pi/6)$

$A=(3*1/4(sqrt6-sqrt2))/(1/2)=3/2(sqrt6-sqrt2)~=1.55$

A triangle has sides A, B, and C. The angle between sides A and B is pi/6pi/6. If side C has a length of 3 3 and the angle between sides B and C is pi/12pi/12, what is the length of side A?