ANSWER
x=24 , y=8√3
EXPLANATION
The given triangle is a right triangle
To find x, we use the cosine ratio, given by:
[tex] \cos(30 \degree) = \frac{adjacent}{hypotenuse} [/tex]
[tex]\cos(30 \degree) = \frac{x}{16 \sqrt{3} } [/tex]
[tex] \frac{ \sqrt{3} }{2} = \frac{x}{16 \sqrt{3} } [/tex]
Solve for x,
[tex]x = \frac{ \sqrt{3} }{2} \times 16 \sqrt{3} [/tex]
[tex]x = 8 \times 3 = 24[/tex]
To find the value of x, we use the sine ratio:
[tex] \sin(30 \degree) = \frac{opposite}{hypotenuse} [/tex]
[tex]\sin(30 \degree) = \frac{y}{16 \sqrt{3} } [/tex]
[tex] \frac{1}{2} = \frac{y}{16 \sqrt{3} } [/tex]
Solve for y to get,
[tex]y = \frac{1}{2} \times 16 \sqrt{3} [/tex]
[tex]y = 8 \sqrt{3} [/tex]
