a)
[tex] {8}^{2} + {6}^{2} = {x}^{2} \\ 64 + 36 = {x}^{2} \\ x = \sqrt{100} = 10[/tex]
b)
[tex] {y}^{2} + {15}^{2} = {17}^{2} \\ {y}^{2} + 225 = 289 \\ {y}^{2} = 64 \\ y = \sqrt{64} = 8[/tex]
c)
[tex] {2}^{2} + {6}^{2} = {z}^{2} \\ 4 + 36 = {z}^{2} \\ 40 = {z}^{2} \\ z = \sqrt{40} = \sqrt{4 \times 10} = 2 \sqrt{10} [/tex]
d)
[tex] {a}^{2} + {4}^{2} = {(3 \sqrt{2}) }^{2} \\ {a}^{2} + 16 = 9 \times 2 \\ {a}^{2} + 16 = 18 \\ {a}^{2} = 2 \\ a = \sqrt{2} [/tex]
