Answer:
x = 33
Step-by-step explanation:
Using the right triangles on the left and right and exact values
sin45° = [tex]\frac{\sqrt{2} }{2}[/tex], tan60° = [tex]\sqrt{3}[/tex]
using right triangle on left then
sin45° = [tex]\frac{opp}{hyp}[/tex] = [tex]\frac{opp}{11\sqrt{6} }[/tex] and
[tex]\frac{opp}{11\sqrt{6} }[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex]
Cross- multiply
2 × opp = 11[tex]\sqrt{12}[/tex] = 22[tex]\sqrt{3}[/tex] ( divide both sides by 2 )
opp = 11[tex]\sqrt{3}[/tex]
Using right triangle on left
tan60° = [tex]\frac{opposite}{adjacent}[/tex]
note the adjacent side is the opposite side of the left triangle, so
tan60° = [tex]\frac{x}{11\sqrt{3} }[/tex] = [tex]\sqrt{3}[/tex], thus
x = 11[tex]\sqrt{3}[/tex] × [tex]\sqrt{3}[/tex] = 11 × 3 = 33
