How to determine the side a of triangle ABC if i know the angle A= 60 degrees and the sides b=square root 3 c=2?

1 Answer

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll have to use the law of cosines to determine the length of the side "a".

a^2 = b^2 + c^2 - 2b*c*cos (b,c) (1)

We know that the side "a" is facing to the angle A, then the side "b" is facing to B and the side "c" is facing to the angle C.

The angle enclosed by the sides "b" and "c" is A.

We know, from enunciation, that A=60 degrees.

Then cos 60 = 1/2

We'll substitute the values of b and c and the cosine of A, into the relation (1).

a^2 = 3 + 4 - 2*sqrt3*2/2

a^2 = 7 - 2sqrt3

a = sqrt(7 - 2sqrt3)

The length of the side "a" is: a = a = sqrt(7 - 2sqrt3).