We need to write an equation relating x (leg CD) to the given data.
The image shows the right triangle ACD, with legs, in ft, given by:
[tex]\begin{gathered} AC=1600 \\ \\ CD=x \end{gathered}[/tex]
Also, angle DAC is 25.4º. Since CD is the opposite leg, and AC is the adjacent leg to this angle, we have:
[tex]\begin{gathered} \tan 25.4\degree=\frac{CD}{AC} \\ \\ \tan 25.4\degree=\frac{x}{1600} \end{gathered}[/tex]
Thus, option A is correct.
Also, we can multiply both sides of the above equation by 1600, to find the equivalent equation:
[tex]\begin{gathered} 1600\cdot\tan 25.4\degree=\frac{x}{1600}\cdot1600 \\ \\ 1600\cdot\tan 25.4\degree=x \\ \\ x=1600\cdot\tan 25.4\degree \end{gathered}[/tex]
Thus, option C is also correct.
Notice that:
[tex]\begin{gathered} \cos 25.4\degree=\frac{AC}{AD} \\ \\ \cos 25.4\degree=\frac{1600^2^{}+x^2}{1600} \end{gathered}[/tex]
Therefore, only options A and C are correct.
