Answer:
[tex]\sqrt{0.5}[/tex]
Step-by-step explanation:
cosx=adj/hyp
adj= [tex]\sqrt{2}[/tex]/2
hyp= r
cos(45)= ([tex]\sqrt{2}[/tex]/2)/r
[tex]\sqrt{2}[/tex]/2 = ([tex]\sqrt{2}[/tex]/2)/r
multiply both sides by r
([tex]\sqrt{2}[/tex]/2)r = [tex]\sqrt{2}[/tex]/2
divide both sides by [tex]\sqrt{2}[/tex]/2
r = 1
pythagorean theorem: [tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
a = [tex]\sqrt{2}[/tex]/2
b = y
c = r = 1
[tex](\sqrt{2}/2)^{2}[/tex] + [tex]y^{2}[/tex] = [tex]1^{2}[/tex]
[tex](\sqrt{2}/2)^{2}[/tex] = 2/4 = 0.5
0.5 + [tex]y^{2}[/tex] = 1
subtract 0.5 from 1
[tex]y^{2}[/tex] = 0.5
[tex]\sqrt{y^{2}}[/tex] = [tex]\sqrt{0.5}[/tex]
y = [tex]\sqrt{0.5}[/tex]
