As suggested, we have to use the law of sines: it states that the ratio between a side and the sine of the opposite angle is constant in every triangle.
We know that one side length is 11, and the opposite angle is 27°
Another side length is 15, and the opposite angle is x.
So, the law of sines states that
[tex]\dfrac{11}{\sin(27)}=\dfrac{15}{\sin(x)}[/tex]
Solving for [tex]\sin(x)[/tex] we have
[tex]\sin(x) = \dfrac{15\sin(27)}{11}[/tex]
Which implies
[tex]x=\arcsin\left(\dfrac{15\sin(27)}{11}\right)[/tex]
Put this into a calculator to get
[tex]\arcsin\left(\dfrac{15\sin(27)}{11}\right)\approx 0.7[/tex]
