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How do you use the law of cosines to find BC given a triangle ABC with Angle A=123, BA=30 and CA=21?

1 Answer

Oct 7, 2016

$B C = 45.02$ $BC=45.02$

Explanation:

Law of cosine : ${(B C)}^{2} = {(A B)}^{2} + {(A C)}^{2} - 2 \cdot (A B) (A C) cos A$ $(BC)^2=(AB)^2+(AC)^2-2*(AB)(AC)cosA$

$\Rightarrow {(B C)}^{2} = 30^{2} + 21^{2} - 2 \cdot 31 \cdot 21 \cdot cos 123$ $=> (BC)^2=30^2+21^2-2*31*21*cos123$

$=>(BC)^2=2874.03....$
$=> (BC)=sqrt(2874.03)$
$=> (BC)=45.02...$

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