+14 First approuch (Theoritical approuch)
Well we have the law of cosine that states: a² = b²+c² - 2bc*cos(A) (where A is the angle across the side a)
We can manipulate this formula to the form of \(A = acos(\frac{(a²-b²-c²)}{-2bc}{})\)
So if we fill in our formula we'll get: \(A = acos(\frac{10²-4²-5²)}{-2*4*5}{})\)
We'd get \(A = acos(-1.475)\), which has no solution
Second approuch (Visual approuch)
You could look at the function \(f(x) = \sqrt{4² + 5² - 2*4*5*cos(x)}\)(where f(x) would be your third side and x would be the angle between the 4- and 5 side)
If you look at the plot of this function you'll see that it never reaches f(x) = 10
Third approuch (intuitional approuch)
A triangle has three sides connected to eachother on their ends -> The sum of two sides must be bigger than or equal to the third side, else there would be no way to connect them to the ends of that side. 4+5 = 9 -> 9 < 10 thus the triangle would be impossible.
Hope this helped!
