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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. – André Nicolas Jun 15 '11 at 18:42

2 Answers

up vote 5 down vote accepted

You would use the Law of cosines

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I just noticed that you already know the law of cosines (or should know it, according to your other question)! cos = adj/hyp is the rule for right triangles, as Ross has mentioned. – The Chaz 2.0 Jun 15 '11 at 18:20
yes yes yes. but which of the two sides is the adj one? – Dan the Man Jun 15 '11 at 18:31
Neither! You will use the law of sines to find the third side, if necessary, and then the law of cosines to find the cosine.... – The Chaz 2.0 Jun 15 '11 at 18:33
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oh! really?? kool. thanks! – Dan the Man Jun 15 '11 at 18:35
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@Dan: My pleasure. Welcome to the site! – The Chaz 2.0 Jun 15 '11 at 18:38
up vote 3 down vote

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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