Anyone able to explain trig q6 please?
Sure, Soysauce.
Try the cosine rule and add the 140 degrees that's there.
I'll explain it better in a minute. Just give me the okay.
Step 1a: Note that the question's looking for "Point C
from A"
Step 1b. (Optional): Instantly eliminate options A and B. A bearing cannot be any smaller than 140 degrees if they've told you B is 140 degrees already. Reminder that you are going from the North and finding the
true bearing. This should be obvious, seeing as none of the options have a direction attached to them.
Step 2a: Rearrange the cosine rule so you can have angle A (or angle CAB, BAC, whatever you call it as long as it's the same one).
Spoiler
Okay, so the cosine rule rearranged will look something like this:
angle A=cos-1((b2+c2-a2)/2bc)
Step 2b.: Use it by substituting the values of b, c and a (the side lengths). Make sure you put in the right ones into the right spots. If you have problems with this, try to label them properly i.e. side b is opposite angle B and so forth.
Spoiler
VCAA decided to use the formula I've just stated. How convenient of them, right?
Therefore:
angle A=cos-1((19002+20502-22502)/2 x 1900 x 2050)
=cos-1(275/779)
=69.3281 degrees(4 decimal places)
Step 3: Hey, we seem to have forgotten something, right?
Spoiler
Simple answer - yes, yes, we definitely have. Some people would have completely forgotten this and, having not crossed out A or B already, would assume it's B... but it's not.
Why?
Spoiler
We've missed our other titbit of information: that 140 degrees.
So, "What's the real answer?" you say with impatience.
Spoiler
We simply have to add them together,
i.e. 140 + 69.3281 = 209.3281 (4 d.p.)
which rounds down to 209 degrees, our closest answer.
It just so happens that this is answer E.
And that, Soysauce, is how we get our answer!
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