Answer:
[tex]x = \frac{ \sqrt{6} }{2} [/tex]
[tex]y = \frac{3 \sqrt{2} }{2} [/tex]
Step-by-step explanation:
[tex] \sin(theta) = \frac{opposite}{hypotenuse} [/tex]
[tex] \cos(theta) = \frac{adjacent}{hypotenuse} [/tex]
[tex] \tan(theta) = \frac{opposite}{adjacent} [/tex]
theta = 30°
hypotenuse = √6
opposite = x
adjacent = y
1) find x using the sin formula
[tex] \sin(theta) = \frac{opposite}{hypotenuse} [/tex]
[tex] \sin(30) = \frac{x}{ \sqrt{6} } [/tex]
[tex] \sin(30) \times \sqrt{6} = x[/tex]
[tex] \frac{ \sqrt{6} }{2} = x[/tex]
[tex]x = \frac{ \sqrt{6} }{2} [/tex]
2) find y using the cos formula
[tex] \cos(theta) = \frac{adjacent}{hypotenuse} [/tex]
[tex] \cos(30) = \frac{y}{ \sqrt{6} } [/tex]
[tex] \cos(30) \times \sqrt{6} = y[/tex]
[tex] \frac{3 \sqrt{2} }{2} = y[/tex]
[tex]y = \frac{3 \sqrt{2} }{2} [/tex]
