In ΔABC, if m = m, m = ß (where ß is an acute angle), and BC = x, which expression gives the length of b, the side opposite?

since we are told ∠A = ∠C we know that ABC is an issueless triangle where AB = BC = x so we get the above diagram. so now, to find side b, we can use the cosine rule which states

c2=a2+b2-2abcosC

so we can apply this to our question, to get,

b2=x2+x2-2 (x) (x) cosß

which simplifies down to

b=√ 2x2-2x2cosß

and you can factor the

2 x 2

to the from to get

b=√ 2 x2 (1-cos ß)