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Sum of the interior angles of any triangle equal 180° .
Thus ;
The angle which facing to the side 4 is 45°.
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Hint :
In a right triangle, the side facing the 45° angle is √2 / 2 times the hypothenuse .
Thus ;
[tex] \frac{ \sqrt{2} }{2} x = 4 \\ [/tex]
Multiply sides by 2
[tex]2 \times \frac{ \sqrt{2} }{2} x = 2 \times 4 \\ [/tex]
[tex] \sqrt{2} x = 8 \\ [/tex]
Divide sides by √2
[tex] \frac{ \sqrt{2}x }{ \sqrt{2} } = \frac{8}{ \sqrt{2} } \\ [/tex]
[tex]x = \frac{4 \times 2}{ \sqrt{2} } \\ [/tex]
[tex]x = \frac{4 \times \sqrt{2} \times \sqrt{2} }{ \sqrt{2} } \\ [/tex]
[tex]x = 4 \sqrt{2} \\ [/tex]
[tex]x = hypothenuse = 4 \sqrt{2} [/tex]
Done...
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