Two sides of an acute triangle are 8 and 15 . How many possible lengths are there for the third side if it is an integer?
According to the Triangle Inequality, the sum of any two sides of a triangle is greater than the third side. Let's call the third side x.
8 + 15 > x --> x < 23
8 + x > 15 --> x > 7
15 + x > 8 --> always true
x has to be between 8 and 22 inclusive, giving us 15 possible side lengths.