Question

1. without using the law of cosines, explain why it is impossible to construct a triangle with lengths 9.6 cm, 12.1 cm, and 23.2 cm.

Explanation:

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. Here, \(9.6 + 12.1=21.7\) cm. Since \(21.7<23.2\), the sum of the two shorter sides (\(9.6\) cm and \(12.1\) cm) is less than the longest side (\(23.2\) cm). This violates the triangle inequality theorem.

Answer:

It is impossible to construct the triangle because \(9.6 + 12.1<23.2\), which violates the triangle - inequality theorem.