Question

Which descriptions can describe more than one triangle? Select two options. side lengths of 6 ft, 8 ft, and 10 ft angle measurements of 35 degrees, 35 degrees, and 110 degrees angle measurements of 30 degrees, 40 degrees, and 50 degrees angle measurements of 40 degrees, 60 degrees, and 80 degrees side lengths of 4 cm, 6 cm, and 9 cm

Answer 1

The descriptions that can describe more than one triangle are:

Side lengths of 6 ft, 8 ft, and 10 ft: This is a classic example of a Pythagorean triple, which means that these side lengths satisfy the Pythagorean theorem and can form a right triangle. There are infinitely many right triangles with integer side lengths that are multiples of this triple, such as 12-16-20, 18-24-30, etc.
Angle measurements of 30 degrees, 40 degrees, and 50 degrees: These angles do not form a unique triangle because they do not determine the side lengths. In fact, there are infinitely many non-congruent triangles that can have these angle measures. This is an example of the ambiguous case of the Law of Sines.