Answer: 19 inches.
Step-by-step explanation:
By definition, an Obtuse angle measures more than 90 degrees and less than 180 degrees. Then, an Obtuse triangle has an angle greater than 90 degrees.
Let be "x" the lenght of the unknown side of the Obtuse triangle.
In this case, knowing the lenght of two sides of the obtuse triangle, we can use the Pythagorean Theorem:
[tex]a^2=b^2+c^2[/tex]
We can say that:
[tex]b=10in\\c=15in[/tex]
Then, solving for "a", we get:
[tex]a=\sqrt{(10in)^2+(15in)^2}=18.02in[/tex]
Then, the smallest possible whole number length of the unknown side of the obtuse triangle is the next whole number greater than 18.02 inches. This is:
[tex]x=19in[/tex]
