Using the law of Sines
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]
Consider the given triangle
Let A = 27°, the a = 11
Let B = 34°, the b = x
Substitute the values into the sine rule formula
This gives
[tex]\frac{\sin27}{11}=\frac{\sin 34}{x}[/tex]
Cross multiply
[tex]x\times\sin 27=11\times\sin 34[/tex]
Divide both sides by sin 27
This gives
[tex]x=\frac{11\times\sin 34}{\sin 27}[/tex]
Solve for x
[tex]\begin{gathered} x=\frac{11\times0.5592}{0.4540} \\ x=\frac{6.1512}{0.4540} \\ x=13.55 \end{gathered}[/tex]
Therefore, the value of x is approximately 13.55
