CONCEPT PREVIEW Assume a triangle ABC has standard labeli...

Question

CONCEPT PREVIEW Assume a triangle ABC has standard labeling.

a. Determine whether SAA, ASA, SSA, SAS, or SSS is given.

b. Determine whether the law of sines or the law of cosines should be used to begin solving the triangle.

a, B, and C

Accepted Answer

Welcome back everyone. In this problem, we let a triangle be labeled as P QR for the measurements that are given that is common PQ and capital R. We want to find out if SA A Sas A SAS S A or SSS is given where S means side and a means angle. Also, we want to state the law which is suitable for solving the triangle for our answer choices A says two sides and an angle is given. So we can use the law of cosines, B says two angles and a side is given. So we can use the law of cosines, C says two sides and an angle are given, we can use the law of S and D says two angles and a side are given, we can use the law of sines. Now, for us to figure out which answer is correct, it would be best for us to try to sketch the triangle to try to visualize what's going on here. So let's imagine that we have a triangle P QR OK. Where let's say that here. That's P, that's Q, that's I. Now we know that these represent angles on our triangle And based on how we usually name triangles. If angle P is here, then the side opposite to angle P would be written or labeled as a common P. Likewise, the side opposite to angle Q would be Q and the side opposite to angle R would be R. Now, what are we given here? Well, we're told that we're given P a common P. So that's the side P, we're also given the side Q and we're given the anger R. So if we were to solve any problems, which law could we use? Well here, notice that we have two sides. OK? And the anger between them and recall that the law of core science tells us get up by the law, of course, signs if we were to use it here for that angle R, then it would tell us that R squared equals P squared plus Q squared minus two PQ multiplied by the cosine of R. So here, once we know those sides and the angle between them, then we could use the law of cosines to help us to figure out the value of R or any other side for that matter. Therefore, the correct answer is a, we're given two sides and an angle and we could use the law of cosines to solve the triangle. Thanks a lot for watching everyone. I hope this video helped.

CONCEPT PREVIEW Assume a triangle ABC has standard labeling.

a. Determine whether SAA, ASA, SSA, SAS, or SSS is given.

b. Determine whether the law of sines or the law of cosines should be used to begin solving the triangle.

a, B, and C

Key Concepts

Triangle Congruence and Similarity Criteria

Law of Sines

Law of Cosines

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