Find the missing length, cosine rule ?

Answer:
Step-by-step explanation:
2abcos C=a²+b²-c²
2×4×x cos 32=4²+x²-3²
8x cos 32=7+x²
x²-8xcos32+7=0
[tex]x=\frac{8 cos 32 \pm\sqrt{(-8cos 32)^2-4*1*7} }{2*1} \\x \approx \frac{6.784\pm 4.246}{2} \\x \approx \frac{6.784+4.246}{2} , \frac{6.784-4.246}{2} \\x \approx 5.515,1.269\\x \approx 5.52,1.27[/tex]