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In the figure if $∠ACB = ∠CDA,\ AC = 8\ cm$ and $AD = 3\ cm$, find BD.
Given: In the figure $\angle ACB =\angle CDA,\ AC = 8\ cm$ and $AD = 3\ cm$.
To do: To find $BD$.
Solution:
![](/assets/questions/media/148618-42033-1616830552.png)
As $\angle CDA=90^o$
$\Rightarrow \angle ACB=90^o$
In $\vartriangle ACD,\ cosA=\frac{AD}{AC}=\frac{3}{8}$
In $\vartriangle ABC,\ cos\theta =\frac{AC}{AB}$
$\Rightarrow \frac{3}{8}=\frac{3}{AB}$
$\Rightarrow AB=8\ cm$
$\Rightarrow BD=8-3$
$=5\ cm$
Thus, $BD=5\ cm$.
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