Calculate distance in a configuration with right angles

Question

In the following figure, it is given three right angles and distances :

$ED = 3 $ , $ EB = 7$ and $CE = 5$.

Is it possible to calculate the length $EA$.

I tried using cyclic quadrilateral $ABCD$ and angles but couldn't find the expression.

thanks for any ideas.

Answer 1

Yes it is. Use the coordinate system. Let $E=(0,0)$, $C = (0,5)$, $B= (-7,0)$ and $D=(3,0)$.

Now you have to calculate $A$ which is in the intersection of lines $AB$ and $AD$ (perpendiculars to $BC$ and $DC$).

Answer 2

I'll solve it trigonometrically using essential concepts like The Law of sines and cosines. EA=5.8 See the link Below https://drive.google.com/file/d/1-OAlQzpJwEDPF7iwhxW575xLe-YbjR5L/view?usp=sharing