Question

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?

Answer 1

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.