What are the values of the variables in the triangle below? If your answer is not an integer, leave it in simplest radical form. The diagram is not drawn to scale. 30 y x 8sqrt3

A x=12sqrt3 y=4****
B x=4 y=12sqrt3
C x=4sqrt3 y=12
D x=12 y=4sqrt3

Help

To find the values of the variables in the triangle, we can make use of the triangle properties and relationships between sides and angles.

In the given triangle, we can see that the sides have lengths of 30, y, and x, and one of the angles measures 30 degrees.

Using the properties of special right triangles, we can identify that the triangle is a 30-60-90 triangle. In a 30-60-90 triangle, the sides are in a specific ratio of x, x√3, and 2x.

Here, the side opposite the 30-degree angle has a length of x, the side opposite the 60-degree angle has a length of x√3, and the hypotenuse has a length of 2x.

Given that one side has a length of 8√3, we can set up an equation to solve for x:

x√3 = 8√3

Dividing both sides by √3:

x = 8

Hence, we find that the side opposite the 30-degree angle, x, has a length of 8.

To find y, we can use the ratio of sides in a 30-60-90 triangle:

y = 2x = 2 * 8 = 16

Therefore, the values of the variables in the triangle are:
x = 8 and y = 16.

So, the correct answer is A: x=8 and y=16.

To determine the values of the variables in the given triangle, we need to analyze the available information.

1. We are given the measures of the three angles in the triangle: 30°, y°, and x°.
2. The value 8√3 corresponds to the length of the side opposite the 30° angle.

Let's analyze the options:

A) x = 12√3, y = 4
B) x = 4, y = 12√3
C) x = 4√3, y = 12
D) x = 12, y = 4√3

To determine the correct option, we need to use the information about the side opposite the 30° angle. In our diagram, the side opposite the 30° angle is labeled 8√3.

This means that the correct option is A) x = 12√3, y = 4.

Use commas to show the sides

I see 30 y x 8sqrt3
is that 30 y, x, 8sqrt3 or .....
What kind of triangle do we have ? right-angled ?