Question

Label all of the missing angle measures1. Given side lengths 3 inches, 7 inches, and 11 inches, can you construct one unique triangle, no triangles, or many triangles? Explain your answer.

Answer 1

The triangle you're describing would be using the lengths of 3 inches, 7 inches, and 11 inches. To determine if these side lengths can form a triangle, you can use the triangle inequality theorem. The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In your case, if we add the lengths of the two shortest sides:

3 inches + 7 inches = 10 inches

This sum is less than the length of the third side (11 inches). Therefore, according to the triangle inequality theorem, these side lengths cannot form a triangle. So, in this case, you can't construct any triangle with the given side lengths.

Answer 2

no triangle

Explanation:

3, 7, 11

In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Add 3 and 7. It must be greater than 11 to have a triangle.

3 + 7 < 11

10 < 11

The sum of 3 and 7 is les than 11, so there is no triangle.