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Answer :

Upandovergo

This is a special kind of right triangle, called a 30-60-90 triangle.

Across from the 30 degree angle, the side is equal to x. Across from the 60 degree angle, the side is equal to x[tex]\sqrt{3}[/tex]. And across from the 90 degree angle, the side is equal to 2x.

Using what we know about 30-60-90 triangles, lets first solve for x. We know that the hypotenuse, given, is equal to 6.

2x = 6

x = 3

Then, we are looking for the side opposite of the 60 degree angle. So its value is  x[tex]\sqrt{3}[/tex].

x = 3

3 *  [tex]\sqrt{3}[/tex] = 3 [tex]\sqrt{3}[/tex]

y =  3[tex]\sqrt{3}[/tex] (option D)

Hope this helps!! :)

The value of y for the given triangle will be  3√3, hence option (D) will be correct.

What is a triangle?

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

Right angle triangles are triangles in which one angle is 90°.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

Given a right-angle triangle

Let the side opposite to 30° is perpendicular and the remaining y will be base.

By trigonometric relation

cosx = base/hypotenuse

cos30° = y/6  

y = 6 × cos30°  ⇒  y = 6 ×  √3/2

y = 3√3 hence the value of the hypotenuse or y will be 3√3.

For more about triangles,

https://brainly.com/question/2773823,

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