Answer:
Option D. [tex]x=45/4\ units[/tex]
Step-by-step explanation:
we know that
In the right triangle ABC
The function cosine of angle C is equal to divide the adjacent side to the angle C (AC) by the hypotenuse (BC)
substitute the values
cos(C)=15/20 ----> equation A
In the right triangle CAD
The function cosine of angle C is equal to divide the adjacent side to the angle C (CD) by the hypotenuse (AC)
substitute the values
cos(C)=x/15 -----> equation B
equate equation A and equation B
[tex]15/20=x/15\\ \\x=15^{2} /20\\ \\x=225/20\ units[/tex]
Simplify
Divide by 5 both numerator and denominator
[tex]x=225/20=45/4\ units[/tex]
