Question

The distance from Jacksonville to Tampa is 171 miles. The distance from Tampa to Miami is 206 miles. Use the triangle inequality theorem to find the range for the distance from Jacksonville to Miami.

Answer 1

The triangle inequality theorem states that any side of a triangle is always shorter than the sum of the two other sides. 
That means if you add up the distance from jacksonville to tampa and the distane from tampa to miami, the distance from jacksonville to miami must be less than that. 

171 miles + 206 miles = 377 miles

the distance from jacksonville to miami must be less than 377 miles