Given the triangle pictured lo the right find the range of v

Given the triangle pictured lo the right, find the range of values that side length x can be such that angle theta will be an obtuse angle.

Solution

One of the angles is greater than 90 degrees
=> a^2 + b^2 < c^2
x is the side opposite the obtuse angle & hence the longest.

Therefore, we have

6^2 + 4^2 < x^2
52 < x^2
7.2 < x
Also x must lie between 6-4 and 6+4 i.e between 2 and 10

Hence the range of x is (7.2,10)