Question

Which three pairs of measurements are possible side lengths for the triangle?

1) 60��, 90��, 30��
2) 60��, 90��, 60��
3) 60��, 30��, 30��
4) 90��, 30��, 30��

Answer 1

To determine the possible side lengths of a triangle, we need to consider the sum of the measures of the three angles. Only option 1) 60°, 90°, 30° is a possible set of side lengths for a triangle.

Step-by-step explanation:

To determine the possible side lengths of a triangle, we need to consider the sum of the measures of the three angles. In a triangle, the sum of the angles is always 180 degrees. Let's examine each option:

1. 60°, 90°, 30°: The sum of these angles is 180°, so this is a possible set of side lengths.
2. 60°, 90°, 60°: The sum of these angles is 210°, which is greater than 180°. Therefore, this is not a possible set of side lengths.
3. 60°, 30°, 30°: The sum of these angles is 120°, which is less than 180°. Therefore, this is not a possible set of side lengths.
4. 90°, 30°, 30°: The sum of these angles is 150°, which is less than 180°. Therefore, this is not a possible set of side lengths.

Based on our analysis, only option 1) 60°, 90°, 30° is a possible set of side lengths for a triangle.