Using relations in right triangles, we find that the value of x is [tex]x = \sqrt{2}[/tex], given by option B.
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- In a right triangle, the sine of an angle is the length of the opposite side divided by the length of the hypotenuse.
In the given triangle:
- The hypotenuse is x.
- Side of length 1 is opposite to an angle of 45º. Thus:
[tex]\sin{45\textdegree} = \frac{1}{x}[/tex]
It is known that [tex]\sin{45\textdegree} = \frac{\sqrt{2}}{2}[/tex], then:
[tex]\frac{\sqrt{2}}{2} = \frac{1}{x}[/tex]
[tex]\sqrt{2}x = 2[/tex]
[tex]x = \frac{2}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}[/tex]
[tex]x = \frac{2\sqrt{2}}{2}[/tex]
[tex]x = \sqrt{2}[/tex]
Thus, option B.
A similar problem is given at https://brainly.com/question/24796576
