In triangle ABC, AC = 6, CB = 8 and angle ACB = 30 degrees. What is the length of side AB

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Given `Delta ABC ` . Let A,B,C be the vertices and a,b,c be the side lengths where a=BC,b=AC and c=AB.

We are given a=8,b=6 and `m/_ ACB=30^@ ` . We are asked to find c=AB.

We know two sides and the included angle of the triangle, so we use the...

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Given `Delta ABC ` . Let A,B,C be the vertices and a,b,c be the side lengths where a=BC,b=AC and c=AB.

We are given a=8,b=6 and `m/_ ACB=30^@ ` . We are asked to find c=AB.

We know two sides and the included angle of the triangle, so we use the Law of Cosines.

Here `c^2=a^2+b^2-2abcosC ` :

`c^2=64+36-2(8)(6)cos30^@ `

`c^2=100-96(sqrt(3)/2)`

` ``c^2~~16.86156` ==> `c~~4.10628 `

Using the law of cosines, we find that the length of side `bar(AB) ` is approximately 4.1

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