Respuesta :

Answer:

Given that the hypotenuse (the side opposite the 90° angle) is √6, we can find the length of the side opposite the 30° angle (which I believe is the side 'a' you're referring to) by dividing the length of the hypotenuse by 2.

So, a = √6 / 2

This is already in simplest radical form with a rational denominator.

Answer:

x = 2[tex]\sqrt{2}[/tex]

Step-by-step explanation:

using the cosine ratio in the right triangle and the exact value

cos30° = [tex]\frac{\sqrt{3} }{2}[/tex] , then

cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{\sqrt{6} }{x}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross multiply )

x × [tex]\sqrt{3}[/tex] = 2[tex]\sqrt{6}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )

x = 2 × [tex]\frac{\sqrt{6} }{\sqrt{3} }[/tex] = 2 × [tex]\sqrt{\frac{6}{3} }[/tex] = 2[tex]\sqrt{2}[/tex]

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