Question

what is a 30-60-90 triangle?
a triangle whose sides are 30, 60, and 90 inches long.
a triangle that has a 30 degree angle, or a sixty degree angle, or a 90 degree angle.
a triangle that has a 30 degree angle, or a sixty degree angle, and a 90 degree angle.
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Explanation:

To determine the correct definition of a 30 - 60 - 90 triangle, we analyze each option:

• Option 1: A 30 - 60 - 90 triangle is defined by its angles, not side lengths of 30, 60, 90 inches. So this is incorrect.
• Option 2: A triangle with just one of 30°, 60°, or 90° is not a 30 - 60 - 90 triangle. A 30 - 60 - 90 triangle must have all three of these angles (since the sum of angles in a triangle is 180°, and 30+60 + 90=180). So this is incorrect.
• Option 3: A 30 - 60 - 90 triangle is a right - angled triangle (has a 90° angle) and also has angles of 30° and 60°, so it has a 30° angle, a 60° angle, and a 90° angle. This matches the definition.

Answer:

The third option: A triangle that has a 30 degree angle, or a sixty degree angle, AND a 90 degree angle.