Answer:
x = 19, y = 19[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Since the triangle is right, we can use the sine and cosine ratios to find x and y
note the exact values of cos60° = [tex]\frac{1}{2}[/tex] and
sin60° = [tex]\frac{\sqrt{3} }{2}[/tex]
cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{38}[/tex]
multiply both sides by 38
x = 38 × cos60° = 38 × [tex]\frac{1}{2}[/tex] = 19
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{y}{38}[/tex]
multiply both sides by 38
y = 38 × sin60° = 38 × [tex]\frac{\sqrt{3} }{2}[/tex] = 19[tex]\sqrt{3}[/tex]