30 60 90 triangle calculator (2023)

They form onetriangleas a geometric shape with three sides and three corners. Theangle ratiotells us what kind of triangle it is. In addition tothe 45 45 90 triangle calculator,you can use this calculatorCalculate 30 60 90 triangles. If we talk about calculators as tools, they make checking the accuracy of calculations much easier. So if you want to know more about what this new calculator brings and what formulas you can use, take a look below.

Suppose you want to expand your knowledge. In that case, don't miss these calculators either:Distance between two parallel lines,segment addition calculator, AndKofunktionsrechner – sin, cos, tan, cot, sec, csc,phase shift calculator.

30 60 90 right triangle set

We can define three basic properties and characteristics to understand the 30-60-90 triangle set. These properties are also expressly described forright triangles. The first property says that the longest side of a triangle is calledthe hypotenusehas in practice always twice the length of the shorter leg. You can also calculate the value of the length of thelonger legMultiply the value of theshorter legby the root number 3. And if you know the values ​​of any side 30-60-90 of the triangle, it will help you to find the values ​​of the unknown sides.

You can mark the value of the shorter leg as y, the value of the hypotenuse as 2y, while the value of the longer leg is:

y\cdot \sqrt{3}

We can emphasize that all triangles 30-60-90 are similar and that two such triangles sharing one long leg thus form an equilateral triangle. Interesting, isn't it?

The figure below shows an example of a 30-60-90 right triangle whose side lengths should always match. Triangle ABC, angle C =30 Grad, Store A =60 Gradand angle B =90 Grad. The side of the triangle is opposite the angle of 30 degrees,AB = y, and as such it is called short leg because it is also the shortest. The side marked opposite the angle of 60 degreesBC = y√3is called the long leg of the triangle, and it is the middle side in length. At the same time, the remaining side of the triangle is also marked the longestAC = 2 years, known as the hypotenuse.

30 60 90 triangle ratio

When determining the 30-60-90 triangle set, it's important to know itratio of sidesof the triangle 30-60-90. Since these are a special type of right triangle, you must always align the lengths of the sides of the triangle so that the ratio of 30-60-90 triangles looks like this:

for pages

1 : √3 : 2 = (y : y√3 : 2y)

or for angles

1 : 2 : 3 = (30° : 60° : 90°)

30 60 90 triangle formula

From a geometric point of view, the formula used for the calculation lies in the basics of trigonometry. If we want to calculate side lengths, we can use a sineStoreof 30 degrees. According to the attached graphic, we can calculate the value of the side lengths b and c using several formulas:

\frac{a}{c} = sin30 = \frac{1}{2}

Woc = 2a

\frac{b}{c} = sin60 = \frac{\sqrt{3}}{2}

Wob = c√3/2

30 60 90 triangle rules and properties

When it comes to the rules you can apply in the 30-60-90 triangle, you will likely manipulate the valuesthe hypotenuseand the shorter legs of the triangle. The geometry is behind all these connections and connections between all three sides of the triangle, and you can see what it looks like in the table below:

Following the properties and rules, one can lose sight of the fact that it's still a triangle. It would help if you never forget that the shape of a triangle is constant under all conditions. Therefore, interior angles should be added180 Grad, while the sides should follow the rules ofPythagorean theorem:

a^{2} + b^{2} = c^{2}

How do we solve a 30 60 90 triangle? - Example

Let us give you a more detailed explanation of the formulas used to calculate each of the cases listed below, and then we will apply the same formulas to a case study.

Solve Part A

If you need the formula to calculate the value of the length of leg A, we can rely on the value of leg b according to the following expression:

a = \frac{b\cdot \sqrt{3}}{3}

Solve Part B

After that, you need to calculate the length of leg B using a formula that looks like this:

b = a\sqrt{3}

Calculate the hypotenuse

Follow the previous explanations and rules related to the longest side of the 30-60-90 triangle, the hypotenuse.
The formula for calculating the hypotenuse looks effortless:

c = 2 \cdot a

Area of ​​a 30-60-90 triangle

The basic formula for calculating theAreaof a two-dimensional shape is the number of square units you need to fill the space inside that shape. In the case of 30-60-90 triangles, the formula you can use to calculate the area of ​​a triangle is:

A = \frac{1}{2}\cdot b\cdot h

where the values ​​are:

A= triangular area
B= base of the triangle
X= height of the triangle

Calculate perimeter

When calculating the perimeter of a triangle of any shape, we need the sum of the edges. therefore, theScopeof the triangle 30-60-90 is equal to the sum of the sides and the hypotenuse. It looks like this:

P = a + b + c

Example:

Now that you are familiar with all the rules, formulas and definitions, you can apply this to the following task:

Find the value of the length of the hypnotic of a right triangle when the value of one side is 8 and the other is 8√3.

8: 8√3 = 1: 1√3

From this mathematical expression we conclude that it was 30-60-90. So we know that the length of the hypotenuse is equal to the value of the small side multiplied by the number 2. From this we can conclude that the hypotenuse value is equal to 16 in this example.

To make the calculation easier, you can use our calculator, which works according to an elementary principle. After accessing ourcalculator, you will see special empty name fields. Regardless of what value you enter, whether side a, side b, or triangular area, the calculator will display results for other blank fields.

FAQ?