Answer:
x = 17[tex]\sqrt{3}[/tex], y = 34
Step-by-step explanation:
Since the triangle is right use trig ratios to find x and y
note exact values sin30° = [tex]\frac{1}{2}[/tex], tan30° = [tex]\frac{1}{\sqrt{3} }[/tex]
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{17}{y}[/tex]
multiply both sides by y
y sin30° = 17 ( divide both sides by sin30° )
y = [tex]\frac{17}{\frac{1}{2} }[/tex] = 34
tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{17}{x}[/tex]
multiply both sides by x
x tan30° = 17 ( divide both sides by tan30° )
x = [tex]\frac{17}{\frac{1}{\sqrt{3} } }[/tex] = 17[tex]\sqrt{3}[/tex]
