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avatar+464 

Here is my question

 

 Oct 15, 2018
 #1
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+1

OK, I will give this a go!

In smaller triangle EFC:

Angle FCE =tan(EF /FC) =tan(FCE)=5/(12 - 5)=5/7

Angle FCE=arctan(5/7) =~35.54 degrees.

 

In the large triangle ABC:

Tan of angle ACB =5/7

5/7 =BA / AC

5/7 =BA / 12

BA =12 x 5/7 =8 4/7 units.

BA - DA =BD

8 4/7 - 5 =3 4/7 units.

 Oct 15, 2018
 #2
avatar+99417 
+1

FC  = 12 - 5  = 7

 

triangle EFC  similar to triangle BDE

 

So we have that

 

EF / FC  = BD / DE

 

5 / 7  = BD / 5

 

BD =  25 /7   [ the same as guest's answer ]

 

 

cool cool cool

 Oct 15, 2018
 #3
avatar+464 
+1

Thank you guys 

 Oct 16, 2018

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