Answer:
12
Step-by-step explanation:
Assume that those angles' curve in the triangle have same measure.
Law of Sin states that:
[tex] \displaystyle \large{ \frac{ \sin A}{a} = \frac{ \sin B}{b} = \frac{ \sin C}{c} = 2R}[/tex]
From the question, assume that B and C are congruent or have same measure. Let B and C be congruent; angle B = angle C thus:-
[tex] \displaystyle \large{ \frac{ \sin B}{b} = \frac{ \sin C}{c} } \\ \displaystyle \large{ \frac{ \sin B}{b} = \frac{ \sin B}{c} } [/tex]
Let b = x and c = 12; for angle B, it's not given so leave it.
[tex] \ \displaystyle \large{ \frac{ \sin B}{x} = \frac{ \sin B}{12} } [/tex]
Multiply both sides by LCM which is 12x.
[tex] \ \displaystyle \large{ \frac{ \sin B}{x}(12x) = \frac{ \sin B}{12}(12x) } \\ \ \displaystyle \large{12\sin B =\sin Bx }[/tex]
Divide both sides by sinB.
[tex] \displaystyle \large{ \frac{12\sin B}{\sin B} = \frac{\sin Bx }{ \sin B}} \\ \displaystyle \large{ 12 = x}[/tex]
Therefore, x = 12.
