Answer:
x= √10/2
Step-by-step explanation:
if you use trig. functions:
sin 45° = opposite side /hypothenuse = x/√5
sin 45° = √2/ 2
√2/2 = x/√5 multiply both sides by √5
x= (√2*√5)/2 = √10/2
if you use that is a 45-45-90 special triangle
the sides are x, and hypothenuse must be x√2 in this type of triangles so in our case:
x√2 = √5 divide both sides by √2
x= √5/√2 multiply by √2/√2 which =1 and help us get rid of the radical from the denominator
x= (√5*√2)/ (√2*√2) = √10/2
