The length of the third of the triangle is 7.76 cm
It is given that the length of the two sides is 6.5 cm and 9.4 cm.
And the angle between them is 131 degrees.
Let a = 6.5 cm
b = 9.4 cm and ∠C = 131 °
According to the law of cosines, we have
[tex]c^{2} = a^{2} +b^{2} -2abcosC\\\\[/tex]
Putting all the given parameters in the given equation, we have
[tex]c^{2} = (6.5)^{2} +(9.4)^{2} -2*6.5*9.4cos131\\\\c^{2} = 42.25 + 90.25 - 72.1497\\\\c^{2} = 60.3503\\\\c = \sqrt{60.3503} \\\\c = 7.76 cm[/tex]
Thus, the length of the third of the triangle is 7.76 cm
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