30 60 90 Triangle Calculator

A 30-60-90 triangle calculator with radicals solves this special right triangle using specific trigonometric formulas for sides and angles.

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 = a√3

Hypotenuse:

Hypotenuse = 2a

Area:

Area = (a²√3) / 2

Perimeter:

Perimeter = a(3 + √3)

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:

b = a√3
c = 2a

a = b / √3
c = (2b) / √3

a = c / 2
b = (c√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√3 : 2a
1 : √3 : 2

How To Solve 30 60 90 Triangle?

Example: Given a hypotenuse (c) of 4, find the other sides (a and b).

Solution:

c = 4
a = c / 2 = 4 / 2 = 2
b = (c√3) / 2 = 2√3 ≈ 3.464

How 30 60 90 Triangle Calculator Works?

Input: Enter any one value into the designated field and click calculate.

Output: The calculator provides the following results:

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

FAQ's:

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 = 180° / (a + b + c)
Angles = 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.