Length of sides in Obtuse triangle

[John26]

Hi, I am a parent trying to help my 15 year old son with the following question,

Question: Calculate the value of x given:
A= 120 deg
a= 26cm
b= x cm
c= 3x cm

Now I assume you need to use the cosine rule but you are only given the the one length and one angle, I have tried to substituet in "x" and "3x" for b and c into the cosine rule.

a^2 = b^2 + c^2 - 2bc * cosA

b=x
c=3x

26^2 =x^2 + 3x^2 - (2 * x * 3x * cos 120 deg)
676 =x^2 + 9x^2 - (6x^2 * -0.5)
676 = 10x^2 - 3x^2
676 = 7x^2
676/7 = x^2
96.57 = x^2
x = 9.83
therefore side AC (b) = 9.83 cm and side AB (c) = 3*9.83 = 29.48 cm which cannot be correct as it can not be longer than side BC (a).
Can you help, am I on the right track or is this completely wrong

Regards
John

 

[Deleted member 4993]

How to calculate the length of sides in an obtuse triangle given:
A= 120 deg
a= 26cm
b= x cm
c= 3x

Hint: Use law of cosines of triangles.

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