Answer:
[tex]x=\frac{7\sqrt{2}}{2}[/tex]
Step-by-step explanation:
The side opposite of the 90 degree angle is the hypotenuse, which is "7".
Now, "x" is the side that is opposite of the 45 degree angle.
So, we have opposite side and hypotenuse.
Which trig ratio relates opposite and hypotenuse??
That is SINE.
So we can write:
Sin(45) = Opposite/Hypotenuse
Sin(45) = x/7
Or,
x = 7 * Sin(45)
Now, from our learning of 45-45-90 triangle, we know that
Sin(45) = [tex]\frac{\sqrt{2}}{2}[/tex]
So, x would be:
[tex]x=7*Sin(45)\\x=7*\frac{\sqrt{2}}{2}\\x=\frac{7\sqrt{2}}{2}[/tex]
This is the simplified form with no radicals in denominator.
