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

This is a right angle

The answer is D x=12, y=4_/3

I'm 100% sure on this, because this is the answer I got when I did the equation, and because I've submitted and this is correct. Hope this helps, Excited.

The four values of the triangle is x and y are the variable, 8 square root 3 is the other side, and the fourth side which freaks you out (Steve) is an angle which is 30°.

Oh triangles, they always try to trick us! But fear not, my dear friend, because this is a simple one:

In the given triangle, we have 30 degrees, y, x, and 8√3. We can use the fact that the angles in a triangle add up to 180 degrees to solve this.

Since we know that one of the angles is 30 degrees, the other two angles must add up to 180 - 30 = 150 degrees.

Now, let's look at the answer choices again:
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 satisfy the condition that the angles add up to 150 degrees, we need the value of y to be greater than x, because the larger angle should be opposite the longer side.

Among the answer choices, only option A) x = 12√3, y = 4 satisfies this condition. Therefore, the values of the variables are x = 12√3 and y = 4.

And voila! We've solved the triangle without breaking a sweat! Well, maybe just a little bit of perspiration.

To determine the values of the variables in the given triangle, we can use a few geometric principles.

First, let's look at the angles in the triangle. We know that the sum of the interior angles in a triangle is always 180 degrees. In this case, we have a 30-degree angle. In a right triangle, the remaining angle must be 90 degrees. Therefore, the remaining angle in this triangle is 180 - 30 - 90 = 60 degrees.

Now, let's focus on the side lengths. The side opposite the 30-degree angle is labeled 8√3. This side can be written as the product of the hypotenuse, x, and the sine of the angle. Therefore, we have:

8√3 = x * sin(30)

To simplify further, we know that sin(30) = 1/2 (or √3/2 in radical form). So, we can rewrite the equation as:

8√3 = x * (1/2)

Now, we can solve for x:

x = (8√3) / (1/2)
x = 16√3

Therefore, we have x = 16√3.

Moving on to the side opposite the 60-degree angle, it is labeled y. This side can be written as the product of the hypotenuse, x, and the cosine of the angle. Thus, we obtain:

y = x * cos(60)

Using the value of x we found earlier, we can simplify it further:

y = (16√3) * cos(60)

We know that cos(60) = 1/2 (or √3/2 in radical form). Therefore, we can rewrite the equation as:

y = (16√3) * (1/2)
y = 8√3

Hence, we find that y = 8√3.

So, the values of the variables in the given triangle are x = 16√3 and y = 8√3, making answer A the correct choice: x = 16√3 and y = 4.

certainly not. It may be a right triangle, but you still offer 4 values. A triangle only has three sides. What oh, what, are the 4 numbers?

Oh, yeah. And what is the question???

as far as I can tell, you didn't correct anything; just threw in a few commas.

You talk about a triangle, but mention 4 values. What is what?