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Help please :) Yr11 3 unit question on trig
In triangle ABC, acosA = bcosB. Prove using the cosine rule, that the triangle is either isosceles or rightangled
 11 months ago
 11 months ago
Help please :) Yr11 3 unit question on trig In triangle ABC, acosA = bcosB. Prove using the cosine rule, that the triangle is either isosceles or rightangled
 11 months ago
 11 months ago

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ajprincessBest ResponseYou've already chosen the best response.2
Do u knw cos rule?
 11 months ago

ajprincessBest ResponseYou've already chosen the best response.2
good:) so vat is cosA?
 11 months ago

ajprincessBest ResponseYou've already chosen the best response.2
Nw if u r to prove that the triangle is isoscles u need to show that a=b or b=c or a=c. if u r to show it is a right angled triangle u should show pythagoras theorem is valid. \[a\cos A=b\cos B\] \[a* \frac{ b^2+c^2a^2 }{ 2bc}=b*\frac{ a^2+c^2b^2 }{ 2ac }\] vat do u get when u simplify this? @AonZ
 11 months ago

AonZBest ResponseYou've already chosen the best response.0
2c^3 a^2  2a^4 c  2c^3 b^2 + 2b^4 c = 0
 11 months ago

ajprincessBest ResponseYou've already chosen the best response.2
u can factor out 2c.
 11 months ago

AonZBest ResponseYou've already chosen the best response.0
2c ( b^4  c^2 b^2 + a^2 c^2  a^4) = 0 this right so far?
 11 months ago

ajprincessBest ResponseYou've already chosen the best response.2
yup:) good:) nw divide by 2c both sides.
 11 months ago

AonZBest ResponseYou've already chosen the best response.0
ok done that. btw im writing it down
 11 months ago

ajprincessBest ResponseYou've already chosen the best response.2
u will get this. b^4  c^2 b^2 + a^2 c^2  a^4=0 try to factorise this.
 11 months ago

AonZBest ResponseYou've already chosen the best response.0
(b^2  a^2)(b^2 +a^2 c^2)
 11 months ago

AonZBest ResponseYou've already chosen the best response.0
(b+a)(ba)(b^2+a^2  c^2)
 11 months ago

ajprincessBest ResponseYou've already chosen the best response.2
(b+a)(ba)(b^2+a^2  c^2)=0 Divide by (b+a)(ba) both sides. vat do u get?
 11 months ago

AonZBest ResponseYou've already chosen the best response.0
you can tell its right angle by looking at this.. but how do you tell if its isosceles?
 11 months ago

ajprincessBest ResponseYou've already chosen the best response.2
u r nt asked to prove both right? either one of that?
 11 months ago

AonZBest ResponseYou've already chosen the best response.0
i still think it means to prove that the triangle must be right or isoscles but it cant be scalene
 11 months ago

AonZBest ResponseYou've already chosen the best response.0
but can we show it isoscles anyways?
 11 months ago

ajprincessBest ResponseYou've already chosen the best response.2
let me think. hav to go nw. will be back in 15 mnts
 11 months ago

gohangoku58Best ResponseYou've already chosen the best response.1
(b+a)(ba)(b^2+a^2  c^2) =0 gives (b+a)=0 OR (ba)= 0 OR (b^2+a^2  c^2)=0 so, ba = 0 >a=b>isosceles (b^2+a^2  c^2)=0 >right as you already know.
 11 months ago

AonZBest ResponseYou've already chosen the best response.0
ohh xDDDD THANKS!! Shame i can only give medal to 1 person :(
 11 months ago

gohangoku58Best ResponseYou've already chosen the best response.1
hey, i am not here for medals ;)
 11 months ago

ajprincessBest ResponseYou've already chosen the best response.2
Welcome:) you can give it to @gohangoku58
 11 months ago

ajprincessBest ResponseYou've already chosen the best response.2
cos he/she deserves it most:)
 11 months ago

gohangoku58Best ResponseYou've already chosen the best response.1
:O You made him solve the whole thing and i deserve it!??
 11 months ago

ajprincessBest ResponseYou've already chosen the best response.2
yup:) it was u who pointed out the isoscles one:)
 11 months ago
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