Question

Determine if each scenario would produce more than one triangle, no triangle, or a unique triangle. Explain your reasoning for each scenario.

A triangle has an angle measuring 90 degrees, and angle measuring 20 degrees, and an included side that is 6 units long.


A triangle with angles measuring 30 degrees, 60 degrees, and 90 degrees.


A triangle with side lengths 2 inches, 4 inches, and 7 inches.

Answer 1

1. Right angle triangle, 2. One triangle, 3. No triangle

Explanation:

1. Has a 90-degree angle which makes it a right-angle triangle.

2. 30 + 60 + 90 = 180 degrees. Hence it satisfies the angle sum property so it is a triangle, a right-angle triangle.

3. It does not form a triangle as it does not satisfy the triangle inequality property, which is the sum of the two smaller sides should be greater than the larger side. 2 + 4 = 6, which is smaller than 7.