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Math Calculators ▶ 45 45 90 Triangle Calculator

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**Table of Content**

The 45 45 90 triangle calculator solves for all sides, area, perimeter, inradius, and circumradius of special right triangles 45 45 90. Enter any of the parameters of your choice and get calculations for all others in seconds and accurately.

**It is a special kind of right triangle in which the measure of two interior angles are 45 degrees and the third one is a right angle (90 degrees).**

Angle Ratios | Side Ratios |
---|---|

1 : 1 : 2 (45° : 45° : 90°) | 1 : 1 : √2 (a : a : a√2) |

The base of the formulas for resolving this triangle comes from trigonometry. And our 45 45 90 triangle calculator considered the following equations for calculating the missing parameters of this right triangle:

As the ratio of the sides is **1:1:√2**, the measure of sides is also done by considering the same ratios:

If the length of a triangle is a, then

- The measure of the second shorter side is also
**“b”** - The measure of the third side opposite to the right angle is as follows:

\(a\sqrt{2}\)

\(Area = \dfrac{a^{2}}{2}\)

You can also get calculations for the area of the sector and semicircles by using another area of a sector calculator and the area of a semicircle calculator.

P = 2a + c = 2b + c

This particular triangle type possesses the following rules:

- A 45 45 90 triangle is also considered an isosceles triangle
- The hypotenuse to the sum of legs ratio is very small for this triangle
- The altitude ratio is maximum when calculated from hypotenuse to the sum of legs

Let’s resolve a 45 45 90 triangle having a shorter side length of 5 cm!

As a 45 45 90 triangle has two equal shorter sides, the second side will also be 5 cm.

Length of side a = 5cm (given)

Length of side b = 5cm (assumed)

Length of longest side = 7.07 cm

The area of 45 45 90 triangle is given as under:

\(Area = a^{2} / 2\)

\(Area = 5^{2} / 2\)

Area = 25 / 2

Area = 12.5 cm

Now we have:

P = 2a + c

P = 2*5+7.07

P = 14.07 cm

The 45 45 90 calculator also generates the same results but saves you a lot of time.

Using our 45 45 90 triangle side calculator is quite straightforward! It requires the following values to calculate results:

**Inputs:**

- Select the parameter from the list
- Now enter its value and select the corresponding unit
- Tap Calculate

**Output:**

- Triangle sides calculations
- Height measurements
- Incircle and circumcircle
- Area & perimeter

We have also developed another 30 60 90 triangle calculator that helps you to calculate missing elements in this special kind of triangle as well.

No! Only two shorter sides of the 45 45 90 triangles are congruent because they measure the same. This is because the triangle is isosceles.

From the source Wikipedia: 45-45-90 triangles, Special right triangle, Angle-based, Side-based, Almost-isosceles Pythagorean triples