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

Algebra ->  Triangles -> SOLUTION: In ΔABC, if m ∠A = m∠C, m∠B = ß (where ß is an acute angle), and BC = x, which expression gives the length of b, the side opposite ∠B ?      Log On


   

Question 966410: In ΔABC, if m ∠A = m∠C, m∠B = ß (where ß is an acute angle), and BC = x, which expression gives the length of b, the side opposite ∠B ?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
By the law of sines,
a%2Fsin%28A%29=b%2Fsin%28B%29=c%2Fsin%28C%29
A=C
.
B=beta
.
a=x
.
A%2BB%2BC=180%7D%7D%0D%0A%7B%7B%7B2A=180-beta
A=90-beta%2F2
So then,
x%2Fsin%2890-beta%2F2%29=b%2Fsin%28beta%29
b=x%2A%28sin%28beta%29%2Fsin%2890-beta%2F2%29%29
highlight%28b=x%2A%28sin%28beta%29%2Fcos%28beta%2F2%29%29%29