Step 1
In the right triangle ABC
Find the cosine angle C
[tex]cos(C)=\frac{AC}{CB}[/tex]
we have
[tex]AC=15\ units\\CB=20\ units[/tex]
substitute
[tex]cos(C)=\frac{15}{20}[/tex] -------> equation A
Step 2
In the right triangle ACD
Find the cosine angle C
[tex]cos(C)=\frac{CD}{AC}[/tex]
we have
[tex]CD=x\ units\\AC=15\ units[/tex]
substitute
[tex]cos(C)=\frac{x}{15}[/tex] -------> equation B
Step 3
Find the value of x
equate equation A and equation B
[tex]\frac{15}{20}=\frac{x}{15} \\ \\x*20= 15^{2} \\ \\ x=\frac{225}{20}[/tex]
Simplify Divide by [tex]5[/tex] both numerator and denominator
[tex]x=\frac{225}{20}=\frac{45}{4}\ units[/tex]
therefore
the answer is
the value of x is [tex]\frac{45}{4}\ units[/tex]
