Consider each case and determine whether there is sufficient i...

Question

Consider each case and determine whether there is sufficient information to solve the triangle using the law of sines.

Three sides are known.

Accepted Answer

Hey, everyone here we are asked to identify whether the following information is sufficient to solve the triangle with the help of the law of signs. Here we have three angles are given, there are two answer, choice options, answer A yes and answer B no. So in order to understand this problem, we first want to sketch a triangle and label its sides and angles. So one side will be labeled lowercase A, the other lowercase B and the third lowercase C. Now labeling the angles opposite from side A, we have angle capital A opposite from side B, we have angle capital B and opposite from C, we have angle capital C. Now recalling the law of signs, we know that sine of capital A divided by lowercase A is equal to sine of capital B divided by lowercase B is equal to s of capital C divided by lowercase C. And now in this scenario, we are assuming that each of the three angles here are known. So looking at our formula, if we have angles, capital A B and C known, we still are missing each of the lengths of each side. So since we are missing all of these signs. There are unlimited possibilities of triangles, regardless the fact that we know all of our angles. Therefore, we know that we do not have enough information given since we are left with infinite possibilities. With only knowing the angles. And with this, we are left with answer choice B where again our final answer is no, we do not have enough information to solve the triangle with the help of the law of signs. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

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Consider each case and determine whether there is sufficient information to solve the triangle using the law of sines.

Three sides are known.