Answer:
[tex] \frac{11}{12} [/tex]
Step-by-step explanation:
[tex]( \sin \theta) ^{2} + ( \cos \theta) ^{2} = 1 \\ \\ \therefore \: { \bigg( \frac{ \sqrt{23} }{12} \bigg)}^{2} + ( \cos \theta) ^{2} = 1 \\ \\ \frac{23}{144} + ( \cos \theta) ^{2} = 1 \\ \\ ( \cos \theta) ^{2} = 1 - \frac{23}{144} \\ \\ ( \cos \theta) ^{2} = \frac{144 - 23}{144} \\ \\ ( \cos \theta) ^{2} = \frac{121}{144} \\ \\ ( \cos \theta) = \sqrt{\frac{121}{144} } \\ \\ \cos \theta = \frac{11}{12} [/tex]
