AonZ
  • AonZ
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 right-angled
Mathematics
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SOLVED
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jamiebookeater
  • jamiebookeater
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ajprincess
  • ajprincess
Do u knw cos rule?
AonZ
  • AonZ
yep...
ajprincess
  • ajprincess
good:) so vat is cosA?

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More answers

AonZ
  • AonZ
b^2 + c^2 - a^2 / 2bc
ajprincess
  • ajprincess
cosB=?
AonZ
  • AonZ
a^2 +c^2 - b^2 / 2ac
ajprincess
  • ajprincess
good:)
ajprincess
  • ajprincess
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. \[a\cos A=b\cos B\] \[a* \frac{ b^2+c^2-a^2 }{ 2bc}=b*\frac{ a^2+c^2-b^2 }{ 2ac }\] vat do u get when u simplify this? @AonZ
AonZ
  • AonZ
2c^3 a^2 - 2a^4 c - 2c^3 b^2 + 2b^4 c = 0
ajprincess
  • ajprincess
u can factor out 2c.
AonZ
  • AonZ
2c ( b^4 - c^2 b^2 + a^2 c^2 - a^4) = 0 this right so far?
ajprincess
  • ajprincess
yup:) good:) nw divide by 2c both sides.
AonZ
  • AonZ
ok done that. btw im writing it down
ajprincess
  • ajprincess
ok:)
ajprincess
  • ajprincess
u will get this. b^4 - c^2 b^2 + a^2 c^2 - a^4=0 try to factorise this.
AonZ
  • AonZ
(b^2 - a^2)(b^2 +a^2 -c^2)
AonZ
  • AonZ
(b+a)(b-a)(b^2+a^2 - c^2)
ajprincess
  • ajprincess
(b+a)(b-a)(b^2+a^2 - c^2)=0 Divide by (b+a)(b-a) both sides. vat do u get?
AonZ
  • AonZ
b^2 +a^2 - c^2 = 0
AonZ
  • AonZ
you can tell its right angle by looking at this.. but how do you tell if its isosceles?
ajprincess
  • ajprincess
u r nt asked to prove both right? either one of that?
AonZ
  • AonZ
oh i guess :)
AonZ
  • AonZ
i still think it means to prove that the triangle must be right or isoscles but it cant be scalene
AonZ
  • AonZ
but can we show it isoscles anyways?
ajprincess
  • ajprincess
let me think. hav to go nw. will be back in 15 mnts
anonymous
  • anonymous
(b+a)(b-a)(b^2+a^2 - c^2) =0 gives (b+a)=0 OR (b-a)= 0 OR (b^2+a^2 - c^2)=0 so, b-a = 0 --->a=b----->isosceles (b^2+a^2 - c^2)=0 --->right as you already know.
AonZ
  • AonZ
ohh xDDDD THANKS!! Shame i can only give medal to 1 person :(
anonymous
  • anonymous
hey, i am not here for medals ;)
ajprincess
  • ajprincess
Welcome:) you can give it to @gohangoku58
ajprincess
  • ajprincess
cos he/she deserves it most:)
anonymous
  • anonymous
:O You made him solve the whole thing and i deserve it!??
AonZ
  • AonZ
lol
ajprincess
  • ajprincess
yup:) it was u who pointed out the isoscles one:)

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