CONCEPT PREVIEW Assume a triangle ABC ha...

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 the triangle be labeled as P QR for the given measurements, capital P, capital Q and R. We want to find out if S A AAA SSA or SS 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 we are given two sides and an angle. So we can use the law of signs B says we are given two angles and a side. So we can use the law of sines. C says we are given two sides and an angle. So we can use the law of cosines. And D says we are given two angles and side so we can use the law of cosines. Now, the best way for us to figure out which law is suitable and what measurements we have is to try and draw the triangle to visualize what our triangle Pqr represents. Now here, let's say that this is triangle P QR. OK. So we know that Pqr, all of these represent angles, angle, P angle Q angle R. And by how we usually name triangles. If P is here, OK, then that means the side opposite to anger P would be called, would be represented as common P. Likewise, the side opposite to anger Q would be Q and the side opposite to anger R would be side R. Now, here it tells us that we know angle P. So let's uh I'm going to put a tick beside that. So we know angle P, we know angle Q, OK? And we know side R, OK. We know side R. So here notice we know two angles and that side. Now let's ask ourselves which law can we use to solve a problem? If we know two angles and the side? Well, here, if we know two angles, OK, then we should be able to figure out the third angle. And when we figure out the third angle, then we'll have a pair of angles and sides. The law of science tells us that the ratio of the sign of the, of an angle to its opposite side in the triangle is the same all throughout. So because we can be able to find that, that means we can use the law of signs. Therefore, the correct answer is and is answer B we have two angles and a side so we can use the law of science. Thanks 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 Criteria (SAA, ASA, SSA, SAS, SSS)

Law of Sines

Law of Cosines

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