# math

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triangle ABC, AB = x cm, BC = (x-4)cm, AC =10 cm and angle BAC = 60° calclulate the value of x

• math -

check out law of cosines

• math -

Triangle ABC
AB = x
BC = x - 4
AC = 10
angle BAC = 60 deg

Using Law of Cosines
a^2 = b^2 + c^2 - 2bc cos A
(x -4)^2 = 10^2 + x^2 - 2(10)(x)cos 60
x^2 - 8x + 16 = 100 + x^2 - 20x (0.5)
x^2 - 8x + 16 = 100 + x^2 - 10x
2x = 84
x = 42

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