SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given sides
[tex]\begin{gathered} a=7.3in \\ b=13.2in \\ c=15.8in \end{gathered}[/tex]STEP 2: Write the formula to calculate the missing angles
To get the missing angles, we use the cosine laws and sine laws stated below:
[tex]\begin{gathered} a^2=b^2+c^2-2bc\cos A \\ b^2=a^2+c^2-2ac\cos B \\ c^2=a^2+b^2-2ab\cos C \\ \\ Sine\text{ law:} \\ \frac{\sin A}{a}=\frac{\sin B}{b}=\frac{sinC}{c} \end{gathered}[/tex]STEP 3: Use the cosine law to find the angle A
[tex]\begin{gathered} a^2=b^2+c^2-2bc\cos A \\ Making\text{ sin A the subject of the formula, we have:} \\ -2bc\cos A=a^2-b^2-c^2 \\ \sin A=\frac{a^2-b^2-c^2}{-2bc} \\ \\ By\text{ substitution,} \\ \cos A=\frac{7.3^2-13.2^2-15.8^2}{-2(13.2\times15.8^)} \\ \cos A=\frac{-370.59}{-417.12}=0.888449367 \\ A=\cos^{-1}0.888449367 \\ A=27.3209628 \\ A\approx27.3^{\circ} \end{gathered}[/tex]Angle A = 27.3 degrees
STEP 4: Find Angle B
Using sine rule, we have:
[tex]\begin{gathered} \frac{\sin A}{a}=\frac{\sin B}{b} \\ By\text{ substitution,} \\ \frac{\sin27.3}{7.3}=\frac{\sin B}{13.2} \\ By\text{ cross multiplication,} \\ sinB\times7.3=sin27.3\times13.2 \\ sinB=\frac{\sin27.3\times13.2}{7.3} \\ \sin B=0.82933892 \\ B=\sin^{-1}0.82933892 \\ B=56.0308892 \\ B=56.1^{\circ} \end{gathered}[/tex]STEP 5: Calculate the Angle C
Recall that the sum of angles in a triangle is 180 degrees, therefore,
[tex]\begin{gathered} A+B+C=180^{\circ} \\ By\text{ substitution,} \\ 27.3^{\circ}+56.1^{\circ}+C=180^{\circ} \\ C=180^{\circ}-27.3^{\circ}-56.1^{\circ} \\ C=180^{\circ}-83.4=96.6^{\circ} \end{gathered}[/tex]Hence, the angles are:
[tex]A=27.3^{\circ},B=56.1^{\circ},C=96.6^{\circ}[/tex]OPTION A