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[tex] \sqrt{ {( - 8)}^{2} + {y}^{2} + {4}^{2} } = 10 \\ \sqrt{64 + {y}^{2} + 16} = 10 \\ \sqrt{80 + {y}^{2} } = 10 \\ 80 + {y}^{2} = {10}^{2} \\ 80 + {y}^{2} = 100 \\ {y}^{2} = 100 - 80 \\ {y}^{2} = 20 \\ y = \sqrt{20} \\ y = 2 \sqrt{5} [/tex]