Respuesta :

One of the rules of triangles is that if you have a 45 45 90 angle triangle, the two sides besides the hypotenuse are equal to each other. In this case, one of the sides is equal to x, so other side is equal to x as well. Now, to solve for x, you need to know the Pythagorean theorum:

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

Both 'a' and 'b' are equal to x, and 'c' is equal to 3, so I'll make the substitutions below:

[tex] {x}^{2} + {x}^{2} = {3}^{2} [/tex]

This can be simplified to:

[tex] {2x}^{2} = 9[/tex]

Now we just solve for x:

[tex] \frac{2}{2} {x}^{2} = \frac{9}{2} [/tex]

[tex] \sqrt{ {x}^{2} } = \sqrt{ \frac{9}{2} } [/tex]

[tex] x = \frac {\sqrt {9}}{\sqrt {2}} \times \frac {\sqrt {2}}{\sqrt {2}} [/tex]

Solution:

[tex] \frac {3\sqrt {2}}{2} [/tex]
akposevictor

Applying the trigonometry ratio SOH, the value of x in the diagram given is: B. [tex]\mathbf{\frac{3\sqrt{2} }{2} }[/tex]

Recall:

  • Any of the trigonometry ratios, SOH CAH TOA, can be applied to solve a right triangle.

Thus, in the diagram shown, the triangle is a right-angled triangle having the following:

  • Reference angle [tex](\theta) = 45^{\circ}[/tex]
  • Hypotenuse length = 3
  • Opposite Length = x

Apply the trigonometry ratio, SOH as follows:

[tex]sin(\theta) = \frac{Opp}{Hyp}[/tex]

  • Substitute

[tex]sin(45) = \frac{x}{3}\\\\\frac{1}{\sqrt{2} } = \frac{x}{3}[/tex](sin 45 = [tex]\frac{1}{\sqrt{2} }[/tex])

  • Multiply both sides by 3

[tex]\frac{1}{\sqrt{2} } \times 3 = \frac{x}{3} \times 3\\\\\frac{3}{\sqrt{2}} = x\\\\x = \frac{3}\sqrt{2}[/tex]

  • Rationalize

[tex]= \frac{3 \times \sqrt{2} }\sqrt{2} \times \sqrt{2}\\\\[/tex]

[tex]\mathbf{x = \frac{3\sqrt{2} }{2} }[/tex]

Therefore, applying the trigonometry ratio SOH, the value of x in the diagram given is: B. [tex]\mathbf{\frac{3\sqrt{2} }{2} }[/tex]

Learn more here:

https://brainly.com/question/11831029

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