Answer:
B
Step-by-step explanation:
using the tangent ratio on the triangle on the right and the exact value
tan60° = [tex]\sqrt{3}[/tex] , then letting the altitude be h
tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{11\sqrt{6} }{h}[/tex] = [tex]\sqrt{3}[/tex] ( multiply both sides by h )
11[tex]\sqrt{6}[/tex] = h × [tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )
11[tex]\sqrt{2}[/tex] = h
using the sine ratio in the triangle on the left and the exact value
sin45° = [tex]\frac{\sqrt{2} }{2}[/tex] , then
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{h}{x}[/tex] = [tex]\frac{11\sqrt{2} }{x}[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ( cross- multiply )
[tex]\sqrt{2}[/tex] × x = 22[tex]\sqrt{2}[/tex] ( divide both sides by [tex]\sqrt{2}[/tex] )
x = 22