Answer:
Option b. [tex]AD=18\ units[/tex]
Step-by-step explanation:
step 1
In the right triangle ABC
Find the sine of angle CAB
[tex]sin(<CAB)=\frac{BC}{AC}[/tex] ---> the sine of angle CAB is equal to divide the opposite side angle CAB (BC) by the hypotenuse (AC)
substitute
[tex]sin(<CAB)=\frac{12}{24}[/tex]
simplify
[tex]sin(<CAB)=\frac{1}{2}[/tex] ---->equation A
step 2
In the right triangle BDC
Find the sine of angle CBD
[tex]sin(<CBD)=\frac{DC}{BC}[/tex] ---> the sine of angle CBD is equal to divide the opposite side angle CBD (DC) by the hypotenuse (BC)
substitute
[tex]sin(<CBD)=\frac{DC}{12}[/tex] ----> equation B
step 3
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
In this problem
Triangles ABC and BDC are similar by AA Similarity Theorem
therefore
m∠CBD≅m∠CAB
equate equation A and equation B
[tex]\frac{DC}{12}=\frac{1}{2}[/tex]
solve for DC
[tex]DC=\frac{12}{2}=6\ units[/tex]
step 4
Find the value of AD
[tex]AD=AC-DC[/tex]
substitute the values
[tex]AD=24-6=18\ units[/tex]
