Answer:
Option C. [tex]BC=31.2\ units[/tex]
Step-by-step explanation:
step 1
In the right triangle ABD find the length side AB
Applying the Pythagoras Theorem
[tex]AB^{2}=5^{2}+12^{2}[/tex]
[tex]AB^{2}=169[/tex]
[tex]AB=13\ units[/tex]
step 2
In the right triangle ABD
we know that
[tex]m<ABD=m<BCD[/tex]
[tex]sin(<ABD)=\frac{5}{13}[/tex] -------> equation A
step 3
In the right triangle ABC
[tex]sin(<BCD)=\frac{13}{5+DC}[/tex] ------> equation B
Remember that
[tex]m<ABD=m<BCD[/tex]
so equate equation A and equation B solve for DC
[tex]\frac{5}{13}=\frac{13}{5+DC}[/tex]
[tex]5(5+DC)=13*13[/tex]
[tex]25+5DC=169[/tex]
[tex]5DC=169-25[/tex]
[tex]5DC=144[/tex]
[tex]DC=144/5=28.8\ units[/tex]
step 4
In the right triangle BDC find the length side BC
Applying the Pythagoras Theorem
[tex]BC^{2}=28.8^{2}+12^{2}[/tex]
[tex]BC^{2}=973.44[/tex]
[tex]BC=31.2\ units[/tex]
