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30 60 90 Triangle Calculator

30 60 90 Triangle Calculator

Enter any known parameter of the 30 60 90 triangle and the calculator will try to calculate all other related parameters.


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Make use of the 30 60 90 triangle calculator with radicals that helps you to solve this special type of right triangle. Except for a normal triangle that may have different measures for sides and angles, you need particular trigonometric formulas to solve for various factors related to this triangle kind.

So let’s get ahead and discuss more about this particular geometrical shape in detail.

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What Is 30 60 90 Triangle?

In trigonometry:

“A triangle having measures of angles equal to 30, 60, and 90 degrees is known as 30 60 90 triangle”


30 60 90 Triangle Formula:

As in a right triangle, we have three sides of different lengths. Now if the longest one is hypotenuse, then we are left with two sides only. Among these two, let’s suppose the shorter side is “a”. We have the following formulas then:

Longer Side:

$$ b = \sqrt{3} $$


$$ Hypotenuse = 2a $$

You can also use another hypotenuse calculator to calculate the hypotenuse of any kind of triangle in a blink of an eye.


$$ Area = a^{2} \frac{\sqrt{3}{2}} $$

Except for this triangle type, you can immediately estimate the area of any geometrical shape by utilising another area calculator.


$$ Perimeter = a\left(3+\sqrt{3}\right) $$

Moreover, it is now possible to determine the perimeter of any geometrical shape by the assistance of a perimeter calculator.

30 60 90 Triangle Side Ratios:

As we have three sides of any triangle, the same is the case in the current situation. Below here we have:

If length a is given:

$$ b = a*\sqrt{3} $$

$$ C = 2a $$

If length of longer side is given that is b:

$$ a = \frac{\sqrt{3}}{3} $$

$$ c = 2b\frac{\sqrt{3}{3}} $$

If only hypotenuse length is given:

$$ a = \frac{c}{2} $$

$$ b = c\frac{\sqrt{3}}{2} $$

30 60 90 Triangle Ratios:

The standard 30 60 90 triangle formula ratios are given as follows:

In case of Angles:

As the angles of the triangle are in the ratio:

$$ 30 : 60 : 90 $$

$$ 1 : 2 : 3 $$

In case of Sides:

30 60 90 triangle side ratios are as follows:

$$ a : a\sqrt{3} : 2a $$

$$ 1 : \sqrt{3} : 2 $$

The online 30 60 90 triangle calculator also takes into consideration these ratios so as to calculate exact results for this particular geometrical figure.

How To Solve 30 60 90 Triangle?

Let’s resolve an example to clarify your mind concept about this special kind of right-angled triangle!

Example # 01:

How to solve a 30 60 90 triangle given as under:


As in the given figure, we have two values X and Y that are unknown, so we are now solving a 30 60 90 triangle given:

$$ c = 4 $$

$$ a = \frac{c}{2} $$

$$ a = \frac{4}{2} $$

$$ a = 2 $$

$$ b = c\frac{\sqrt{3}}{2} $$

$$ b = 4\frac{\sqrt{3}}{2} $$

$$ b = 4*0.866 $$

$$ b = 3.464 $$

For cross check, you may subject to this fully fledged 30 60 90 triangle sides calculator.

How 30 60 90 Triangle Calculator Works?

This free 30 60 90 triangle solver is very simple to use. Want to learn its operation? Okay let’s go!


  • Just enter any one of the inputs in its designated fields and hit the calculate button


The online 30-60-90 triangle calculator does the following computations:

  • Length of second side
  • Hypotenuse
  • Area
  • Height
  • Perimeter
  • Inradius
  • Circumradius

Related: You may also try our 45 45 90 triangle calculator to solve for each and every value in this right triangle.

But what to do if you are dealing with any other triangle type? Do not worry as we have the best solution for this. Yes, we are talking about nothing but a detailed triangle calculator that helps you to determine all parameters of any triangle kind.


How do you find the ratio of a triangle?

To find the ratios of any triangle, you need to follow up the following key points in your mind:

  • First of all, calculate the value of x for angles by following the expression:

$$ x = \frac{180^\text{o}}{a+b+c} $$

  • Then find the product of x with all angle sone by or as follows:

$$ a*x, b*x, c*x $$

Moreover, you can also find the ratios for the sides of any triangle by using the law of sines calculator.

What is the 3 4 5 Triangle rule?

The 3 4 5 rule of triangle states that:

“If the length of one side of triangle is 3 and of adjacent side is 4, then the length of the diagonal joining them must be 5”

The online 30 60 90 triangle calculator with radicals also does the same calculations but saving you a lot of time.

Does 9 12 and 15 make a right triangle?

According to the pythagorean theorem, if the sum of the squares of the short sides becomes equal to the square of the hypotenuse length, then the set of sides makes a perfect right triangle. And 9 12 and 15 make a perfect right angled triangle.

Does 5 12 and 13 make a right triangle?

Yes, three of these numbers make a right triangle. This is because they are pythagorean triplets.


Triangles are very crucial to understand and resolve for their parameters. The reason is that many other geometrical figures such as polygons having 4, 5, or even 6 sides can be reduced to triangle, this provides an instant approach to the manual calculations of the triangle thus further creating ease in simplifying the polygons. And rest when fast calculations are concerned, the 30 60 90 triangle calculator is the only best choice you are left with. So stop thinking and start making use of this calculator.


From the source of Wikipedia: Triangle, Types of triangle, Basic facts, Right triangles, Existence of a triangle, Points, lines, and circles associated with a triangle, Computing the sides and angles, Euclidean triangles

From the source of Khan Academy: angles in triangles, Isosceles & equilateral triangles problems, Angles

From the source of Lumen Learning: A Bit of Geometry, Similar Triangles, Areas