We have been a right triangle. We are asked to find the missing length of the given triangle.
We can see that our given triangle is 30-60-90 triangle.
We know that the lengths of the sides of a 30-60-90 triangle are in the ratio [tex]1:\sqrt{3}:2[/tex].
If the side opposite to 30 degree is [tex]n[/tex], then the side opposite to 60 degree angle will be [tex]\sqrt{3}n[/tex] and side opposite to hypotenuse will be [tex]2n[/tex].
We can see that side corresponding to hypotenuse is 6 that is [tex]2n=6[/tex].
Let us solve for n.
[tex]\frac{2n}{2}=\frac{6}{2}[/tex]
[tex]n=3[/tex]
The side corresponding to 30 degree angle will be half of 6 that is 3. Therefore, the value of y is 3.
The value of x will be [tex]3\sqrt{3}[/tex] as it is side corresponding to 60 degree angle.
