Answer:
Option D
Step-by-step explanation:
According to law of cosines =
[tex] {a}^{2} = {b}^{2} + {c}^{2} - 2bc. \cos(A) [/tex]
where 'a' is the uknown side , 'b' & 'c' are the given sides and angleA is the angle opposite to the uknown side i.e. opposite to 'a'.
Using the Law of cosines , we'll find the length of AC .
[tex] {ac}^{2} = {7}^{2} + {13}^{2} - 2 \times 7 \times 13 \times \cos(50) [/tex]
[tex] = > {ac}^{2} = 49 + 169 - 182 \times 0.76[/tex]
[tex] = > {ac}^{2} = 218 - 138.8 = 79.68[/tex]
[tex] = > ac = \sqrt{79.68} = 8.92 = 9(appx)[/tex]
In option D , if we'll round of 8.86 , then its appx 9. So option D is right
