Cosine rule

  • Thread starter Natasha1
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  • #1
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Homework Statement


In triabgle ABC, AB = 2x cm, AC = x cm, BC = 21 cm and angle BAC = 120 degrees. Calculate the value of x?

Homework Equations


I used the cosine rule here

The Attempt at a Solution


As we have 2 sides and an angle I used the cosine rule - Am I correct?
(2) means squared

b(2) = a(2) + c(2) - 2ac cos B
so
x(2) =21(2) + (2x)(2) - 2.21.2x.c cos B
x(2) =441 + 4x(2) - 84x cos B
3x(2) = 84x cosB - 441

How do I find x from here?
 

Answers and Replies

  • #2
Merlin3189
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Why did you choose to use angle B ?
Since you know angle A, wouldn't that be easier?
 
  • #3
Samy_A
Science Advisor
Homework Helper
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Homework Statement


In triabgle ABC, AB = 2x cm, AC = x cm, BC = 21 cm and angle BAC = 120 degrees. Calculate the value of x?

Homework Equations


I used the cosine rule here

The Attempt at a Solution


As we have 2 sides and an angle I used the cosine rule - Am I correct?
(2) means squared

b(2) = a(2) + c(2) - 2ac cos B
so
x(2) =21(2) + (2x)(2) - 2.21.2x.c cos B
x(2) =441 + 4x(2) - 84x cos B
3x(2) = 84x cosB - 441

How do I find x from here?
Applying the cosine rule is the way to go.
But you should apply it correctly, with the angle you know (that's angle A):
##a²=b²+c²-2bc\cos(A)##, where a is the side opposite angle A, b the side opposite angle B and c the side opposite angle C.
You also know ##\cos(A)=\cos(120°)##.
 
Last edited:
  • #4
467
7
Thanks everyone, I have found that x(2) = 63 which makes x = 7.94 cm (to 2dp) using the cosine rule

Am I correct?

a(2) = b(2) + c(2) - 2bc cos B
so
21(2) =x(2) + (2x)(2) - 2.x.2x cos B
441 = 5x(2) - 4x(2) cos 120
441 = x(2) (5-4 cos 120)
x(2) = 441 / (5-4cos 120)
x(2) = 63
x = 7.94 cm (to 2dp)
 
  • #5
Samy_A
Science Advisor
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Thanks everyone, I have found that x(2) = 63 which makes x = 7.94 cm (to 2dp) using the cosine rule

Am I correct?

a(2) = b(2) + c(2) - 2bc cos B
so
21(2) =x(2) + (2x)(2) - 2.x.2x cos B
441 = 5x(2) - 4x(2) cos 120
441 = x(2) (5-4 cos 120)
x(2) = 441 / (5-4cos 120)
x(2) = 63
x = 7.94 cm (to 2dp)
Looks correct (except that the angle should better be called A, not B).
 

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