Answer:
x = 10[tex]\sqrt{2}[/tex] , y = 10[tex]\sqrt{6}[/tex]
Step-by-step explanation:
using the sine and cosine ratios in the right triangle and the exact values
cos60° = [tex]\frac{1}{2}[/tex] , sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , then
cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{20\sqrt{2} }[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2x = 20[tex]\sqrt{2}[/tex] ( divide both sides by 2 )
x = 10[tex]\sqrt{2}[/tex]
and
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{y}{20\sqrt{2} }[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
2y = 20[tex]\sqrt{2}[/tex] × [tex]\sqrt{3}[/tex] = 20[tex]\sqrt{6}[/tex] ( divide both sides by 2 )
y = 10[tex]\sqrt{6}[/tex]
