The answer is 5√2
We can use trigonometric functions to solve for the missing side. Since adjacent is what is missing, then we can use this formula:
[tex]cosA = Adjacent/Hypotenuse[/tex]
From the problem we know that:
x = adjacent
Hypotenuse =10
A = 45°
So we plug in the data into the formula and derive the adjacent side.
[tex]cosA = Adjacent/Hypotenuse[/tex]
[tex]cos45 = x/10[/tex]
[tex](10)cos45 = x[/tex]
The exact value of [tex]cos45 = \frac{ \sqrt{2} }{2} [/tex].
[tex](10)(\frac{ \sqrt{2} }{2})= x[/tex]
[tex]5 \sqrt{2} =x[/tex]
