Answer:
Option D) 64
Step-by-step explanation:
see the attached figure with letters to better understand the problem
In the right triangle BCD find BC
Applying the Pythagoras Theorem
[tex]BC^{2}=48^{2}+36^{2}\\BC^{2}=3,600\\BC=60\ units[/tex]
In the right triangle ABC
[tex]cos(C)=BC/AC[/tex]
substitute the values
[tex]cos(C)=60/(x+36)[/tex] -------> equation A
In the right triangle BDC
[tex]cos(C)=CD/BC[/tex]
substitute the values
[tex]cos(C)=36/60[/tex] -------> equation B
equate equation A and equation B
[tex]60/(x+36)=36/60\\ \\(x+36)*36=60*60\\ \\36x+1,296=3,600\\ \\36x=3,600-1,296\\ \\36x=2,304\\ \\x=64\ units[/tex]
