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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:

- Reach (codomain) of cosine is - 1 ≤ cos(α) ≤ 1
- Cosine period is equivalent to 2π
- It's an even capacity (while sine is odd!), which implies that cos(- α) = cos(α)
- Cosine definition is fundamental to comprehend the law of cosines - a valuable law to settle any triangle.

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