The value of x is 6
"It is a triangle in which one of the angle measures 90° "
"It is the longest side of the right triangle."
"In a right triangle [tex]a^{2} +b^{2}= c^{2}[/tex] where c is the hypotenuse and a, b are other two sides of the right triangle."
"In a right triangle, sine of angle is the ratio of the opposite side of angle to the hypotenuse."
For given question,
For given right triangle, first we find the sine of angle 45° whose opposite side is 6 units.
[tex]\Rightarrow sin(45)=\frac{6}{y}\\\\\Rightarrow \frac{1}{\sqrt{2} }=\frac{6}{y} \\\\\Rightarrow y=6\sqrt{2}[/tex]
Now, using Pythagoras theorem we find the value of x
[tex]\Rightarrow x^{2} + 6^2=y^2\\\\\Rightarrow x^{2} + 36 = (6\sqrt{2} )^2\\\\\Rightarrow x^{2} + 36 = 36\times 2\\\\\Rightarrow x^{2} +36=72\\\\\Rightarrow x^{2} = 72-36\\\\\Rightarrow x^{2} = 36\\\\\Rightarrow x = 6[/tex]
Therefore, the value of x is 6
Learn more about the sine angle here:
brainly.com/question/13256520
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