In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
triangles diagram
Step 02:
We must analyze the figure to find the solution.
triangle ABC:
∠ A + ∠ B + ∠ C = 180°
∠ A + 30 + 90 = 180
∠ A = 180 - 90 - 30 = 60
∠ A = 60°
BC:
[tex]\begin{gathered} cos\text{ 30 = adjacent / hypotenuse} \\ \\ cos\text{ 30 = }\frac{BC}{16\text{ }\sqrt{3}} \end{gathered}[/tex]
BC = 24
AC:
AC = opposite
[tex]\begin{gathered} sin\text{ B = opposite / hypotenuse} \\ \\ sin\text{ 30 = }\frac{AC}{16\sqrt{3}} \\ \\ 16\sqrt{3}*sin\text{ 30 = AC} \\ \\ 13.86\text{ = AC} \end{gathered}[/tex]
triangle ACD:
opposite = BD
adjacent = AC
BD:
[tex]\begin{gathered} tan\text{ 30 = opposite / adjacent } \\ \\ tan\text{ 30 = }\frac{DC}{13.86} \\ \\ 13.86\text{ * tan 30 = DC} \\ \\ \text{8 = DC} \\ \\ BD\text{ = 24 - 8 = 16} \end{gathered}[/tex]
The answer is:
BD = 16
