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:



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, $BD=5\ cm$.

Updated on: 10-Oct-2022

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