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Maths A Level Cosine Rule/ Algebra question watch

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    Hi! I’m having trouble working out this question:
    In triangle ABC, AB=x cm, BC=(x+2) cm, AC= 5cm and angle ABC=60°. Find the value of x.
    I have to use the cosine rule to work this out (and maybe the sine rule - triangle formulas basically) but I end up getting 42=0 which doesn’t give me x and doesn’t make sense! Can someone help me with this?
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    (Original post by geometric)
    Hi! I’m having trouble working out this question:
    In triangle ABC, AB=x cm, BC=(x+2) cm, AC= 5cm and angle ABC=60°. Find the value of x.
    I have to use the cosine rule to work this out (and maybe the sine rule - triangle formulas basically) but I end up getting 42=0 which doesn’t give me x and doesn’t make sense! Can someone help me with this?
    Well, when you plug in the values to the cosine rule, you should get:

    25=x^2+(x+2)^2-2x(x+2)(cos(60))
    cos(60)=1/2, so that simplifies to

    25=x^2+(x+2)^2-x(x+2)

    This eventually simplifies down to:
    0=x^2+2x-21
    which will give two answers of which one is positive.

    See calculation below:
    https://www.wolframalpha.com/input/?...2)%5E2-x(x%2B2)
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    (Original post by TheGuy264)
    Well, when you plug in the values to the cosine rule, you should get:

    25=x^2+(x+2)^2-2x(x+2)(cos(60))
    cos(60)=1/2, so that simplifies to

    25=x^2+(x+2)^2-x(x+2)

    This eventually simplifies down to:
    0=x^2+2x-21
    which will give two answers of which one is positive.

    See calculation below:
    https://www.wolframalpha.com/input/?...2)%5E2-x(x%2B2)
    Thank you so much!!! My mistake was not halving the part connected with cos60 as it’s equal to 1/2
 
 
 

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