Answer:
b. [tex]x=69,\ y=23\sqrt{3}[/tex]
Step-by-step explanation:
The diagram shows the right triangle with an acute angle of [tex]30^{\circ}.[/tex]
In [tex]30^{\circ}-60^{\circ}-90^{\circ}[/tex] right triangle, the leg opposite to the [tex]30^{\circ}[/tex] angle is half the hypotenuse, so
[tex]y=\dfrac{1}{2}\cdot 46\sqrt{3}=23\sqrt{3}[/tex]
By the Pythagorean theorem,
[tex]x^2+y^2=(46\sqrt{3})^2\\ \\x^2=(46\sqrt{3})^2-(23\sqrt{3})^2\\ \\x^2=46^2\cdot 3-23^2\cdot 3=23^2\cdot 3(4-1)\\ \\x^2=23^2\cdot 3^2\\ \\x=23\cdot 3=69[/tex]
