Given are the lengths of two sides of a triangle. find the range of lengths for the third side
7,10

The triangle inequality theorem states that any side of a triangle is always shorter than the sum of the two other sides. 

so if the two other sides are 7 and 10, the sum of the two other sides is 17 (7+10=17)

therefore, the third side must be shorter than 17

The third side must be greater than  3, otherwise it couldn't reach
the ends of the 7 and 10.

Also, it must be less than  17, otherwise the 7 and 10 couldn't reach
the ends of it.