Answer:
Part 1) [tex]x=\frac{10\sqrt{3}}{3}\ units[/tex]
Part 2) [tex]y=5\ units[/tex]
Step-by-step explanation:
step 1
Find the value of x
In the right triangle of the figure
[tex]sin(30^o)=\frac{(5\sqrt{3}/3)}{x}[/tex] ---> opposite side angle of 30 degrees divided by the hypotenuse
Remember that
[tex]sin(30^o)=\frac{1}{2}[/tex]
substitute
[tex]\frac{1}{2}=\frac{(5\sqrt{3}/3)}{x}[/tex]
solve for x
[tex]x=\frac{5\sqrt{3}}{3}(2)[/tex]
[tex]x=\frac{10\sqrt{3}}{3}\ units[/tex]
step 2
Find the value of y
In the right triangle of the figure
[tex]cos(30^o)=\frac{y}{x}[/tex] ---> adjacent side angle of 30 degrees divided by the hypotenuse
we have
[tex]x=\frac{10\sqrt{3}}{3}\ units[/tex]
[tex]cos(30^o)=\frac{\sqrt{3}}{2}[/tex]
substitute
[tex]\frac{\sqrt{3}}{2}=\frac{y}{\frac{10\sqrt{3}}{3}}[/tex]
[tex]y=(\frac{\sqrt{3}}{2})(\frac{10\sqrt{3}}{3})[/tex]
[tex]y=5\ units[/tex]
