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How would you calculate the cosine of an obtuse triangle's largest angle?

Cos = adj/hyp. But which side is the adjacent side?

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    "How would you calculate" is not clear enough. You did post a diagram, which is helpful. But you did not indicate **what is known** about the triangle. Is it the three sides? If that is the case, say so, and give the measurements. Is it one angle and two sides? The more specific you are, the more quick and relevant will be the response.2011-06-15

3 Answers 3

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You would use the Law of cosines

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    @Dan: My pleasure. Welcome to the site!2011-06-15
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Cosine=adjacent/hypotenuse is only true in right triangles, as that is the only time there is a hypotenuse. $\cos \theta$ is well defined for $\theta \gt 90^{\circ}$ and we have $\cos \theta=-\cos (180^{\circ}-\theta)$.

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$\cos A= -\cos(180-A)$ e.g $\cos(120)= -cos(180-120)= -\cos60$ i.e $-1/2$ or $-0.5$

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    This could work if you knew the measure of angle $A$, but presumably that was not the case the OP had in mind when presenting the illustration of a triangle. See the Accepted Answer for a more likely interpretation.2015-09-11