The maximum angle measure in an acute triangle can be 90°. In such a case we would have [tex] a^{2} + b^{2} = c^{2} [/tex]
Now forget about side c, and open the angle between a and b just a little bit. Now clearly [tex]a^{2} + b^{2}[/tex] is larger that [tex]c^{2}[/tex] because the "new c" is larger than the old one.
2. So for 3 numbers to be the lengths of the sides of an acute triangle, the sum of the squares of the 2 smaller numbers must be at most equal to the square of the largest number but not more.
Check:
A. 4^2+5^2=16+25=41<49 B. 5^2+7^2=25+49=74>64 C. 6^2+7^2=36+49=85<100 D. 7^2+9^2=49+81=130<144
