Answer:
x = 4[tex]\sqrt{3}[/tex] , y = 4
Step-by-step explanation:
using the cosine and sine ratios in the right triangle and the exact values
cos30° = [tex]\frac{\sqrt{3} }{2}[/tex] , sin30° = [tex]\frac{1}{2}[/tex] , then
cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{8}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
2x = 8[tex]\sqrt{3}[/tex] ( divide both sides by 2 )
x = 4[tex]\sqrt{3}[/tex]
and
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{y}{8}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2y = 8 ( divide both sides by 2 )
y = 4
