MATH SOLVE

4 months ago

Q:
# Find the missing sides.

Accepted Solution

A:

Answer:Part 3) [tex]x=6\ units[/tex][tex]y=3\ units[/tex]Part 4) [tex]x=18\sqrt{2}\ units[/tex]Step-by-step explanation:Part 3) step 1Find the value of xIn the right triangle of the figure we know thatThe cosine of angle of 30 degrees is equal to the adjacent side to angle of 30 degrees divide by the hypotenuseso[tex]cos(30\°)=\frac{3\sqrt{3}}{x}[/tex]and remember that[tex]cos(30\°)=\frac{\sqrt{3}}{2}[/tex]substitute[tex]\frac{\sqrt{3}}{2}=\frac{3\sqrt{3}}{x}[/tex]Simplify[tex]x=(2*3)=6\ units[/tex]step 2Find the value of yIn the right triangle of the figure we know thatThe sine of angle of 30 degrees is equal to the opposite side to angle of 30 degrees divide by the hypotenuseso[tex]sin(30\°)=\frac{y}{x}[/tex]and remember that[tex]sin(30\°)=\frac{1}{2}[/tex]substitute[tex]\frac{1}{2}=\frac{y}{6}[/tex][tex]y=6/2=3\ units[/tex]Part 4) Find the value of xApplying the Pythagoras Theorem[tex]x^{2} =18^{2} +18^{2} \\ \\x^{2} = 324+324\\ \\x^{2}=648\\ \\x=\sqrt{648}\ units[/tex]Simplify [tex]x=18\sqrt{2}\ units[/tex]