Answer: Hello there!
You can see that this is a triangle rectangle, where one of the catheti is equal to 5, and we know all the angles (you can see that both lower angles are equal to 45°, then is safe to assume that both catheti are equal in length, but let's do the math):
we need to find the length of the other cathetus and the length of the hypotenuse.
A very useful thing to remember when you are working with a triangle rectangle is:
So-Ca -Toa
this means:
sin(a) = (opposite cathetus)/(hipotenuse)
cos(a) = (adjacent cathetus)/(hipotenuse)
tan(a) = (opposite cathetus)/(adjacent cathetus)
now, we can find y using the third relation:
tan(45°) = 5/x
y= 5/tan(45°) = 5
because tan(45°) = 1
and this has a lot of sence, because you can see that both cathetus are symetric.
Now we can find the value of x with the next Pythagorean theorem:
the square hypotenuse is equal to the sum of the squares of the cathetus:
x^2 = 5^2 + 5^2 = 2*(5^2)
x= (√2)*5
then the right answer is option B:
x = (√2)*5 and y = 5