To find the angle θ, we are to apply the method of Cosine of angles.
[tex]\begin{gathered} \cos \theta=\frac{adjacent}{hypotenuse} \\ \text{adjacent}=\text{ BC=10} \\ \text{hypotenuse}=AB=16 \\ \end{gathered}[/tex][tex]\begin{gathered} \cos \theta=\frac{10}{16}=0.625 \\ \cos \theta=0.625 \\ \theta=\cos ^{-1}0.625 \\ \theta=51.3^0 \end{gathered}[/tex]The total angle in a triangle=180.
So to get the remaining angle we need to add 90° to 51.3° and subtract them from 180°.
180°-(90°+51.3°)
180°-141.3°= 38.7°
An acute angle is an angle less than 90°, so therefore 51.3° is the largest acute angle.
Hence, option D is the right answer.
