Answer:[tex]\dfrac{3}{2}[/tex]
Step-by-step explanation:
Tangent of an angle in right angled triangle is defined as the ratio of opposite side to adjacent side.
In triangle [tex]CAB[/tex],
Given that [tex]CB=1[/tex] and [tex]AB=2[/tex]
tan([tex]CAB[/tex])=[tex]\frac{CB}{AB}[/tex]=[tex]\frac{1}{2}[/tex]
In triangle [tex]BAD[/tex],
Given [tex]AD=3[/tex]
tan([tex]BAD[/tex])=[tex]\frac{BD}{AD}[/tex]=[tex]\frac{BD}{3}[/tex]
Since,angle [tex]BAD[/tex] is same as angle [tex]CAB[/tex],their tangents are equal.
[tex]\frac{1}{2}=\frac{BD}{3}[/tex]
So,[tex]BD=\frac{3}{2}[/tex]
