Answer:
see explanation
Step-by-step explanation:
Using the exact values of the trigonometric ratios
sin30° = [tex]\frac{1}{2}[/tex], cos30° = [tex]\frac{\sqrt{3} }{2}[/tex]
Then
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{17}{y}[/tex] = [tex]\frac{1}{2}[/tex]
Cross- multiply
y = 2 × 17 = 34
cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{y}[/tex] = [tex]\frac{x}{34}[/tex] and
[tex]\frac{x}{34}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
2x = 34[tex]\sqrt{3}[/tex] ( divide both sides by 2 )
x = 17[tex]\sqrt{3}[/tex]
Hence
x = 17[tex]\sqrt{3}[/tex] and y = 34
