Question

Determine whether each triangle below will form a unique triangle, no triangle, or more than one triangle based on the criterion given.

Part A:

A triangle with 5 cm and 7 cm side lengths and an included 50∘ angle will form
.



Part B:

A triangle with side lengths 3 inches, 2 inches, and 1 inch will form
.



Part C:

A triangle with angle measures of 72°, 24°, and 84∘ will form

Answer 1

A. a unique triangle

B. no triangle

C. more than one triangle

Answer 2

9514 1404 393

Answer:

A: a unique triangle

B: no triangle

C: more than one triangle

Explanation:

A: Two sides and the included angle are sufficient to completely specify one triangle. (See the first attachment.)

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B: The given side lengths do not satisfy the triangle inequality. No triangle can be formed. (See the second attachment.)

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C: The angles total 180°, so a triangle can be formed with those angles. However, the side lengths are not specified, so any number of triangles can be made with those angles.