Question

With the lengths of two sides of a triangle and the measure of the angle between the two sides, is it possible to construct the triangle? A) No, because it is impossible to know the length of the third side. B) Yes, because there can be only one possible length of the third side. C) No, because it is impossible to know the measures of the other two angles. D) Yes, because the sum of the measures of the other two angles must be 180°.

Answer 1

B. 2 sides and and angle determine a triangle but there ASA postulate

Answer 2

Answer: B) Yes there's only one possible length for the third side

By the SAS (side angle side) congruence rule for triangles, we know that only one triangle is possible. So only one side length is possible for that third missing side. We can use the law of cosines to figure out the length of the missing side.