Question

In triangle PQR = 7.2 and = 5.2. Which measure cannot be ?

Answer 1

Use the triangle inequality. One side is 7.2, and the other side is 5.2. Imagine a triangle with these two sides and a very small angle between them. The last side would have to be 7.2 - 5.2 = 2 units long. Now imagine a triangle with these two sides with 180 degrees between them. The last side would have to be 7.2 + 5.2 = 12.4 units long. We know that the real side length must be between these two extremes, so any measure more than 12.4 or less than 2 cannot be the length of the last side.