An acute triangle had two sides measuring 8cm and 10 cm what is the best representation of the possible range of values for tge third side, s?

The third side must be >2 and < 18

To test if a triangle is acute, right or obtuse:

1) Square all 3 sides

2) Sum the squares of the 2 shortest sides

3) Compare this sum to side 3 squared

if sum > side 3 squared it is an acute triangle

if sum = side 3 squared it is a right triangle

if sum < side 3 squared it is an obtuse triangle

The shortest side 2 can be is "less than 2" so we'll say it is 2.00000001

three sides squared =

4.00000004

64

100

Summing the 2 shortest sides 4.00000004 + 64 = 68.00000004

68.00000004 is less than 100 so it is an obtuse triangle no matter how long the third side is.