a
(a)The horizontal components are \({({B_H})_1} = B\cos {\phi _1}\)and \({({B_H})_2} = B\cos {\phi _2}\)
\(\therefore \,\frac{{{{({B_H})}_1}}}{{{{({B_{^H}})}_2}}} = \frac{{\cos {\phi _1}}}{{\cos {\phi _2}}} = \frac{{\cos {{30}^o}}}{{\cos {{45}^o}}} = \frac{{\sqrt 3 }}{2} \times \sqrt 2 = \frac{{\sqrt 3 }}{{\sqrt 2 }}\)