Question

Please help i’m so confused!

Answer 1

Answer:$\dfrac{3}{2}$

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 $CAB$,

Given that $CB=1$ and $AB=2$

tan($CAB$)=$\frac{CB}{AB}$=$\frac{1}{2}$

In triangle $BAD$,

Given $AD=3$

tan($BAD$)=$\frac{BD}{AD}$=$\frac{BD}{3}$

Since,angle $BAD$ is same as angle $CAB$,their tangents are equal.

$\frac{1}{2}=\frac{BD}{3}$

So,$BD=\frac{3}{2}$