Answer:
[tex]\begin{gathered} AT=8\sqrt[]{3} \\ AC=8 \\ mStep-by-step explanation:To find the missing lengths of the triangle, use trigonometric ratios for right triangles, which are represented by the following equations:
[tex]\begin{gathered} \sin (\text{angle)=}\frac{\text{ opposite}}{\text{ hypotenuse}}_{} \\ \cos (\text{angle)}=\frac{\text{adjacent}}{\text{hypotenuse}} \\ \tan (\text{angle)}=\frac{\text{ opposite}}{\text{ adjacent}} \end{gathered}[/tex]Then, find the opposite and adjacent side given the 60 degrees angle:
[tex]\begin{gathered} \sin (60)=\frac{AT}{16} \\ AT=16\cdot\sin (60) \\ AT=8\sqrt[]{3} \\ \\ \cos (60)=\frac{AC}{16} \\ AC=16\cdot\cos (60) \\ AC=8 \end{gathered}[/tex]Now, since the intern angles of a triangle must add up to 180 degrees, given two of the angles find the missing angle:
[tex]\begin{gathered} m