A source of laser light sends rays AB and AC toward two opposite walls of a hall. The light rays strike the walls at points B and C, as shown below:

The smallest possible whole-number length of the unknown side = 19 inches

Step-by-step explanation:

Given : Two sides of the obtuse triangle , 10 inches and 15 inches

Now, let the third side be x and this side is given to be the longest side

And in an obtuse triangle :

Square of longest side > Sum of square of other two sides

⇒ x² > 10² + 15²

⇒ x² > 100 + 225

⇒ x² > 325

⇒ x > ±18.03

Since the length cannot be negative

⇒ x > 18.03 ≈ 19 ( whole-number )

Hence, the smallest possible whole-number length of the unknown side = 19 inches