Answer
(a)Acute Triangle
(b)Right Triangle
(c)Obtuse Triangle
Work Step by Step
(a) substitute: a=4, b=5, c=6,
$4^{2}$+$5^{2}$?$6^{2}$
16+25?36
41$\gt$36
$a^{2}$+$b^{2}$$\gt$$c^{2}$ is an acute triangle
(b)Substitute: a=3, b=4, c=5
$3^{2}$+$4^{2}$? $5^{2}$
9+16?25
25=25
$a^{2}$+$b^{2}$=$c^{2}$ is a right triangle
(c)Substitute a=10, b=15, c=20
$10^{2}$+$15^{2}$? $20^{2}$
100+225? 400
325$\lt$400
$a^{2}$+$b^{2}$$\lt$ $c^{2}$ is Obtuse
