Answer:
x = 11, y = 22
Step-by-step explanation:
Using the tangent ratio in the right triangle and the exact value
tan60° = [tex]\sqrt{3}[/tex] , then
tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{11\sqrt{3} }{x}[/tex] = [tex]\sqrt{3}[/tex] ( multiply both sides by x )
11[tex]\sqrt{3}[/tex] = x × [tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )
11 = x
Using Pythagoras' identity in the right triangle
y² = x² + (11[tex]\sqrt{3}[/tex] )² = 11² + 363 = 121 + 363 = 484 ( square root of both sides )
y = [tex]\sqrt{484}[/tex] = 22
