Tickbox Quiz 11 #8

In the solution, this question is solved using similar triangles. I’m curious to why it isn’t solvable just finding angles and using 30-60-90?

I was solving it using that and found that angle C was 30, angle A was 60. And BC = 8. So it looked like with 8 as the hypotenuse, I found that BD was 4. But then with 6 as the other smaller triangle’s hypotenuse, the BD was not 4 but it gave me 3 root 3.

Can someone explain why it’s not solvable using this method?

How?

Oh sorry, I think I got confused!

I thought for a second that if the pythagorean theorem works, it is a 30-60-90 triangle but I think the angles has nothing to do with the pythagorean theorem.

Am I correct?

That.