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Answer:

[tex]c=\sqrt{65}=8.062.[/tex]

Step-by-step explanation:

[tex]\text{Consider } \bigtriangleup DBC, \text{by Pythagoras}\\DB^2+BC^2=DC^2 \\\Rightarrow b^2=DC^2-BC^2\\\Rightarrow b^2= 5^2-3^2=25-9\\\Rightarrow b^2= 16\\\text{Then } , b=4.\\ \text{Consider } \bigtriangleup DBA, \text{by Pythagoras}\\DB^2+BA^2=DA^2\\\Rightarrow c^2=b^2+BA^2\\\Rightarrow c^2=4^2+7^2\\\Rightarrow c^2=16+49\\\Rightarrow c^2=65\\\text{Then } , c=\sqrt{65}=8.062.[/tex]

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