A triangle has sides A, B, and C. Sides A and B are of lengths $7$ $7$ and $4$ $4$ , respectively, and the angle between A and B is $\frac{π}{6}$ $pi/6$ . What is the length of side C?

Question

1499 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-06-25T20:54:30

$C = \sqrt{65 - 28 \sqrt{3}} = \sqrt{16.51} ≅ 4.06 .$ $C=sqrt(65-28sqrt3)=sqrt16.51~=4.06.$

We use Cosine-rule for $DeltaLMN : n^2=l^2+m^2-2*l*m*cos/_(l,m).$

$:. C^2=A^2+B^2-2A*B*cos/_(A,B)=49+16-56cos(pi/6)=65-56*(sqrt3/2)=65-28sqrt3~=65-48.49=16.51.$

$:. C=sqrt16.51~=4.06.$

A triangle has sides A, B, and C. Sides A and B are of lengths 777 and 444, respectively, and the angle between A and B is pi/6π6pi/6. What is the length of side C?