At store A a trophy costs $12.50. Engraving costs $0.40 per letter. At store B, the same trophy costs $14.75. Engraving
costs $0.25. How many letters must be engraved for the cost at
store B to be less expensive?

Given:

Two sides of a triangle are 14 and 23.

To find:

The angle for the measures for the third side of a triangle.

Solution:

If a, b, c are three sides of a triangle, then

It is given that two sides of a triangle are 14 and 23.

Let the third side of the given triangle be c. Then, using the above inequalities, we get

                ...(i)

Similarly,

                ...(ii)

And,

                ...(iii)

Using (i), (ii) and (iii), we get

Therefore, the range for third side of the triangle is .