Question

Why cannot this length be determined?

In triangle DEF, the length of DE is `sqrt(30)` inches and the length of EF is 3 inches. If it can be determined, what is the length, in inches, of DF?

The answer is that the length cannot be determined from the given information...why is this?

Answer 1

See below.

Explanation:

There are infinitely many triangles that can be built given two sides.

Think, for example, of a circle. Consider the radius connecting the center `O` to a fixed point `P`. Then, consider any other radius, connecting the center to a variable point `Q`. You have all the possible triangles `OPQ` as `Q` runs over the circumference, and you always know that `OP` and `OQ` have length `r`, but `PQ` varies.

If you want to solve this problem, you need to know the angle between the two sides, and from there you could solve the triangle.