We have the triangle and we must find the value of x.
To find the value of x we need to use the Law of Sines
- a is the opposite side to the angle A
- b is the opposite side to the angle B
- c is the opposite side to the angle C
So, seeing the triangle we can take values as
angle A = 27°, so a = 11
angle B = 34°, so b = x
Replacing in the law of Sines
[tex]\frac{\sin27\degree}{11}=\frac{\sin34\degree}{x}[/tex]
Finally, we must solve the equation for x
[tex]\begin{gathered} \frac{\sin27\degree}{11}=\frac{\sin34\degree}{x} \\ \sin 27\degree\cdot x=\sin 34\degree\cdot11 \\ x=\frac{\sin 34\degree\cdot11}{\sin 27\degree} \\ x=13.5 \end{gathered}[/tex]
ANSWER:
x = 13.5
