So confused…

At school we are doing trigonometry and I got given some questions and I am stuck on one of them.

I have worked out that OB is 4 because 8x sin (30) = 4 but triangle DBC isn’t right angled so I don’t know how to work it out. I would appreciate some help. Also, I am not just using TSR to do all my homework it is just this one question that I can’t figure out.

Edit, this is due tomorrow so I would appreciate help

I think I am correct in saying that triangle BCD is a right angle as the angle at the circumference of a semicircle is always 90°. Therefore, you can work out that the diameter of the circle (DB) is 8cm and then use CAH to work out that BC is 3.63cm (3 s.f.). I hope this makes sense and is helpful

Triangle DBC is right angled because angles in a semi-circle are 90 degrees

Oh ok I was thinking that it needed the right angle symbol to be a right angle. Thanks

Yeah, sometimes they intentionally don't add it. Like they didn't explicitly tell you that DB is the diameter or that ABD was a right angle bc of the tangent/radius, you just had to know that.

I'd recommend trying to memorise circle theorems (whether by flashcard or other) to the point that when you see a circle question, your first instinct is the note the theorems involved