Answer:
Options A and D.
Explanation:
It is given in the question
Side AC = 6.9 cm
side BC = 9.8 cm
side AB = 12 cm
Let ∠BAC = x
We can find this angle x by applying sine and cosine rule in the given right angle triangle ABC
sinx =
![\frac{\text{opposite side}}{\text{Hypotenuse}}=(BC)/(AB)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/7tbu46d1hdnwif1oxy6v2zffbo7s39e8sa.png)
=
![(9.8)/(12)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/at3a1gb6imvoqfrjvldd4k5nieiohv0wp0.png)
![x = sin^(-1)[(9.8)/(12)]](https://img.qammunity.org/2019/formulas/mathematics/middle-school/c98ii0knv014aovmmivndd9r7l4wthjjdc.png)
Now we apply cosine rule
cosx =
![\frac{\text{Adjacent side}}{\text{Hypotenuse}}](https://img.qammunity.org/2019/formulas/mathematics/middle-school/kf5ivfdxozs2idig6ttbh43cj9a54jqyqt.png)
=
![(6.9)/(12)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/9h9fyz20xlkuyccpap0rupqqt71w9fhpvj.png)
x =
![cos^(-1)((6.9)/(12) )](https://img.qammunity.org/2019/formulas/mathematics/middle-school/bew04ywl1o6ay0gie9w1673aatu7jjxul5.png)
Therefore, options A and D are the correct options.