Answer:
[tex]x = 3\sqrt 2[/tex]
Step-by-step explanation:
Given
See attachment
Required
Find x
To solve for x, we simply apply sine formula which states:
[tex]sin\ (\theta) = \frac{Opposite}{Hypotenuse}[/tex]
In this case:
[tex]\theta = 45^{\circ}[/tex]
[tex]Opposite = 3[/tex]
[tex]Hypotenuse = x[/tex]
So, the formula becomes:
[tex]sin(45) = \frac{3}{x}[/tex]
Cross Multiply
[tex]x * sin(45) = 3[/tex]
Make x the subject
[tex]x = \frac{3}{sin(45)}[/tex]
[tex]sin(45) = \frac{1}{\sqrt 2}[/tex]
So, we have:
[tex]x = \frac{3}{\frac{1}{\sqrt 2}}[/tex]
[tex]x = 3/\frac{1}{\sqrt 2}[/tex]
[tex]x = 3 * \sqrt 2[/tex]
[tex]x = 3\sqrt 2[/tex]
