Question

Suppose you are given information about a triangle according to SSS, SAS, and ASA. For which of these can you immediately use the Law of Cosines to find one of the remaining measuress?????

Answer 1

Answer:

If you're only allowed one answer, then I'd say the best answer is SAS. If multiple answers are allowed, then SSS can be included.

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Explanation:

With SSS, you can use the law of cosines to find any or all of the three angles. You'll have to do a bit of algebra to isolate the angle.

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With SAS, you can use the law of cosines

Law of cosines

c^2 = a^2+b^2 - 2ab*cos(C)

we have 'a' and 'b' as the two sides, with C as the included angle (it is between sides 'a' and 'b')

Don't forget to apply the square root to both sides to fully isolate the missing side c.

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You cannot use the law of cosines with ASA. There isn't enough information. However, you can use the law of sines to figure out the other side lengths. Keep in mind that you'll need to determine the third missing angle first.

Answer 2

Answer:

SSS and SAS

Step-by-step explanation:

Law of cosines: The law of cosines is used for calculating one side of a triangle when the angle opposite and the other two sides are known.

If the information about a triangle according to SSS, SAS and ASA is given, then we will immediately use SSS and SAS  by using the law of cosines to find one of the remaining measures because Law of cosines is applied if we know one angle opposite and the other two sides.

Also, in ASA, we know two angles and one side, thus we cannot use Law of cosines in this, rather Law of sines can be accurately use in this case.

if you have two sides, encroaching an angle, then the Law of Cosines can be used to find a missing side, thus SAS will work fine for that, now, if you have no angles given, but you know all sides, you can use the Law of Cosines as well, by solving it for the angle, and get the angles, on which case, SSS will do... .now as far as ASA, if you have two angles and one side known, then... that's not very workable for the law of cosines

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