Answer:
x = [tex]\sqrt{6}[/tex] , y = 2[tex]\sqrt{3}[/tex]
Step-by-step explanation:
using the tangent ratio and the exact value tan45° = 1 , then
tan45° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{\sqrt{6} }[/tex] = 1 , then
x = [tex]\sqrt{6}[/tex]
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using the cosine ratio in the right triangle and the exact value
cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then
cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{\sqrt{6} }{y}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
y = [tex]\sqrt{6}[/tex] × [tex]\sqrt{2}[/tex] = [tex]\sqrt{12}[/tex] = 2[tex]\sqrt{3}[/tex]
