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$$a=8$$ $$b=11$$ $$c=37$$
We know angle \(C =\ 37º,\ and\ sides\ a =\ 8\ and\ b =\ 11\) The Law of Cosines says: \(c^2\ =\ a^2 + b^2 − 2ab\ cos(C)\) Put in the values we know: \(c^2 = 82 + 112 − 2 × 8 × 11 × cos(37º)\) Do some calculations: \(c^2 = 64 + 121 − 176 × 0.798…\) More calculations: \(c^2 = 44.44...\) Take the square root: \(c = √44.44 = 6.67\) Answer: \(c = 6.67\)
$$c^2=a^2 + b^2 − 2ab\ cos(C)$$
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Cosine is perhaps the most fundamental mathematical capacities. It very well might be characterized based on the right triangle or unit hover, in analogical route as the sine is characterized:
The cosine of a point is the length of the adjoining side partitioned by the length of the hypotenuse.
cos(α) = nearby/hypotenuse = b/c
Right triangle: delineation of the cosine definition. Adjoining side over a hypotenuse.
In case you don't know what the contiguous and hypotenuse is (and inverse, also), look at the clarification in the sine adding machine.
The name cosine comes from a Latin prefix co-and sine work - so it is a real sense implies sine supplement. What's more, in reality, the cosine capacity might be characterized that way: as the sine of the correlative point - the other non-right point. The shortening of cosine is cos, for example, cos(30°).
Significant properties of a cosine work:
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