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AonZ

  • 2 years 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 right-angled

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  1. ajprincess
    • 2 years ago
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    Do u knw cos rule?

  2. AonZ
    • 2 years ago
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    yep...

  3. ajprincess
    • 2 years ago
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    good:) so vat is cosA?

  4. AonZ
    • 2 years ago
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    b^2 + c^2 - a^2 / 2bc

  5. ajprincess
    • 2 years ago
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    cosB=?

  6. AonZ
    • 2 years ago
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    a^2 +c^2 - b^2 / 2ac

  7. ajprincess
    • 2 years ago
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    good:)

  8. ajprincess
    • 2 years ago
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    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

  9. AonZ
    • 2 years ago
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    2c^3 a^2 - 2a^4 c - 2c^3 b^2 + 2b^4 c = 0

  10. ajprincess
    • 2 years ago
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    u can factor out 2c.

  11. AonZ
    • 2 years ago
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    2c ( b^4 - c^2 b^2 + a^2 c^2 - a^4) = 0 this right so far?

  12. ajprincess
    • 2 years ago
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    yup:) good:) nw divide by 2c both sides.

  13. AonZ
    • 2 years ago
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    ok done that. btw im writing it down

  14. ajprincess
    • 2 years ago
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    ok:)

  15. ajprincess
    • 2 years ago
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    u will get this. b^4 - c^2 b^2 + a^2 c^2 - a^4=0 try to factorise this.

  16. AonZ
    • 2 years ago
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    (b^2 - a^2)(b^2 +a^2 -c^2)

  17. AonZ
    • 2 years ago
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    (b+a)(b-a)(b^2+a^2 - c^2)

  18. ajprincess
    • 2 years ago
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    (b+a)(b-a)(b^2+a^2 - c^2)=0 Divide by (b+a)(b-a) both sides. vat do u get?

  19. AonZ
    • 2 years ago
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    b^2 +a^2 - c^2 = 0

  20. AonZ
    • 2 years ago
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    you can tell its right angle by looking at this.. but how do you tell if its isosceles?

  21. ajprincess
    • 2 years ago
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    u r nt asked to prove both right? either one of that?

  22. AonZ
    • 2 years ago
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    oh i guess :)

  23. AonZ
    • 2 years ago
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    i still think it means to prove that the triangle must be right or isoscles but it cant be scalene

  24. AonZ
    • 2 years ago
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    but can we show it isoscles anyways?

  25. ajprincess
    • 2 years ago
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    let me think. hav to go nw. will be back in 15 mnts

  26. gohangoku58
    • 2 years ago
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    (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.

  27. AonZ
    • 2 years ago
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    ohh xDDDD THANKS!! Shame i can only give medal to 1 person :(

  28. gohangoku58
    • 2 years ago
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    hey, i am not here for medals ;)

  29. ajprincess
    • 2 years ago
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    Welcome:) you can give it to @gohangoku58

  30. ajprincess
    • 2 years ago
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    cos he/she deserves it most:)

  31. gohangoku58
    • 2 years ago
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    :O You made him solve the whole thing and i deserve it!??

  32. AonZ
    • 2 years ago
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    lol

  33. ajprincess
    • 2 years ago
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    yup:) it was u who pointed out the isoscles one:)

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