Hello from MrBillDoesMath!
Answer:
x = 5 * sqrt(2)
5 = y
Discussion:
First thing: the hypotenuse is the side opposite the right (90 degree) angle. So it is side x NOT side y as shown in your diagram.
The triangle is a 45-45-90 triangle so
tan(45) = y/5 => as tan(45) = 1
1 = y/5 => multiply both sides by 5
5 = y
If you don't care for the trig approach, since it's a 45-45-90 triangle the length of the legs are that same, i.e y = 5
Also sin(45) = y/x => as y = 5
sin(45) = 5/x => as sin(45) = sqrt(2)/2
sqrt(2)/2 = 5/x => multiply bot sides by x
x* sqrt(2)/2 = 5/x * x = 5 =>
x* sqrt(2)/2 = 5 => divide both sides by sqrt(2)/2
x = 5 * (2/sqrt(2))
x = 5 * sqrt(2)
Or if you don't care for the trig approach, simply apply the Pythagorean theorem ( 5^2 + 5^2 = x^2) and solve for x
Thank you,
MrB