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# Maths A Level Cosine Rule/ Algebra question watch

1. 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?
2. (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)
3. (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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Updated: February 24, 2018
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