Take into account the length of the right side of the figure is 10. Moreover, x is the hypotenuse of a right triangle. To find the value of x, use the sine function:
cos 45 = opposite side/hypotenuse
cos 45 = 10/x solve for x
x = 10/cos 45
x = 10/0.707
x = 14.14
with the previous value of x, you can find y. Again, consider the right triangle right side. x is the hypotenuse. Use the Pythagorean theorem to find y:
x² = 10² + y² solve for y and replace x
y² = x² - 10²
y² = (14.14)² - 100
y² = 200 - 100
y² = 100 apply square root both sides
y = 10
Hence, the values of x and y are 14.14 and 10 respectively