Stuck on trigonometry question

[Zeeflyboy]

I can't for the life of me understand why complicating the problem with unnecessary equations and factorisation. I gave the solution in post 2, using basic trigonometry.

Probably because you didn't give the solution... After he's split it in the second diagram the only angle you know on the right hand side triangle (for which you have the actual length value you suggest to use) is the 90 degree... what you suggest with reverting to "basic" trig with one angle and a side only works because for a right angle triangle the 90 is a given - for your idea you would need to use another angle other than the 90 (Either C, or A - 30) to solve the green line, which you don't have.

 

[explicit4u]

Route 73 is usually there to throw you, if they don't ask for an answer to the nearest significant figure or something along those lines there's no need to work out the actual answer. Write out the cosine rule, sub in what you know, then see if there's any way to fiddle with the equation to make it easier to work out X.

These questions always threw me in exams because i'd spend too much time working out all the values before realising it was pointless!

 

[Psiko]

Probably because you didn't give the solution... After he's split it in the second diagram the only angle you know on the right hand side triangle (for which you have the actual length value you suggest to use) is the 90 degree... what you suggest with reverting to "basic" trig with one angle and a side only works because for a right angle triangle the 90 is a given - for your idea you would need to use another angle other than the 90 (Either C, or A - 30) to solve the green line, which you don't have.

You can actually do this but it’s more complicated than just using the cos rule as has already been suggested. In fact, dropping a perpendicular in this way is one way of deriving the cosine rule. You end up with the bottom horizontal (AC in the diagram) being split in to x/2+1 to the left of the perpendicular (because it is sin30=1/2 of the hypoteneuse) and 3x/2-4 on the right (such that the sum of the two is 2x-3 as required). The height of the perpendicular is root3/2 (x+2) (because it is cos60 = root3/2 times the hypoteneuse). You can then apply Pythagoros to the right right-angled triangle and you end up with the same quadratic as touch derived (and hence the same answer of x=6 (or -3 which is obviously not possible)). Like I say, it’s easier to just use the cosine rule as this method basically derives the cosine rule.

 

[Zeeflyboy]

Sure, but that is just another way of skinning the same poor old cat. I was responding to his claim that you don’t need any of the, to quote, “unnecessary equations and factorisation” touch did, you can just use “basic trigonometry” and that the best solution was thus offered in the second post.

My statement was simply that you cannot solve it in the simple way he suggested, so he did not offer a solution as claimed… any talk of mole wrenches and screws was therefore misplaced and touch did a lovely job of solving it.

 

[dl8860]

Substitute into the cosine rule formula and sort it from there.

a^2 = b^2 + c^2 - 2bccosA

Just did it using this method and got a sensible answer. You can do it OP.

edit: Just saw @touch did it above, I agree with that.

@Old Joe Soap if it's so easy using your way, why not follow through with the actual numbers for it? Quite funny bashing the correct method as overcomplicated and yours as some sort of clever way when you don't actually show how to do it.

 

[lemonkettaz]

I'm intrigued to know of the quick trig method.... as I can't see it but be nice to be shown...

 

[Blackjack Davy]

I really should have said in my opening post, I'm not good at maths, not even at GCSE level. I just don't have the knowledge of how to do what you're suggesting :O
I figured my answer would need to involved trigonometry rules, but perhaps that's where I'm going wrong - it's just another area of basic maths I need to know.

Do you? Do you really? I can't imagine any useful application of this knowledge outside of engineering or technical drawing etc. Knowledge for knowledge sake is fine if you find it interesting lord knows I love reading history especially ancient history but maths bores me and I have no aptitude whatsoever.