The right angled triangles ABD and BCD?

Question

AB=5cm BD=4cm and angle ABD=x

Find the exact value of cos(ABC)

this is the trangle...: https://twitter.com/JxstyBiebs/status/432919494466752514

Answer 1

Use $cos(ABC) = cosxcos90 - sinxsin90$ by sum formula. But $cos90=0$ and $sin90=1$ so we are left with finding $sinx$ which is basic right angle trig. Think of SOHCAHTOA. My screen shed tears with that J Bieber picture. Next time, please warn us :)