Answer:
x = 5 , y = 5[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Using the sine and cosine ratios in the right triangle and exact values.
sin30° = [tex]\frac{1}{2}[/tex] , cos30° = [tex]\frac{\sqrt{3} }{2}[/tex] , then
sin30°= [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{10}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2x = 10 ( divide both sides by 2 )
x = 5
and
cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{y}{10}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
2y = 10[tex]\sqrt{3}[/tex] ( divide both sides by 2 )
y = 5[tex]\sqrt{3}[/tex]
