Answer: [tex]x=7 sqrt(6)\ \ or\ x=7\sqrt{6}[/tex]
Step-by-step explanation:
For this exercise you can use the following Trigonometric Identity:
[tex]sin\alpha =\frac{opposite}{hypotenuse}[/tex]
In this case you can identify in the figure given in the exercise that:
[tex]\alpha =45\°\\\\opposite=7\sqrt{3}\\\\hypotenuse=x[/tex]
Knowing those values, you must substitute them into [tex]sin\alpha =\frac{opposite}{hypotenuse}[/tex], as following:
[tex]sin(45\°)=\frac{7\sqrt{3}}{x}[/tex]
Now you must solve for "x" in order to find its value.
You need to remember that, by definition:
[tex]sin(45\°)=\frac{1}{\sqrt{2}}[/tex]
Therefore, you get that the value of "x" is:
[tex](x)(\frac{1}{\sqrt{2}} )=7\sqrt{3}\\\\x=(7\sqrt{3})( \sqrt{2}})\\\\x=7\sqrt{6}}[/tex]
