45 45 90 triangle calculator is a dedicated tool to solve this special right triangle. Find out what are the sides, hypotenuse, area, and perimeter of your shape and learn about the 45 45 90 triangle formula, ratio, and rules. If you want to know more about other popular right triangles, check out this 30 60 90 triangle calculator and special right triangles calculator.
If you are wondering how to find the formula for 45 45 90 triangle hypotenuse, you're at the right place.
OK, looks easy, but where does it come from? There are a couple of methods to prove that equation, the most popular between them are:
Did you notice that the 45 45 90 triangle is half of a square, cut along the square's diagonal?
If you heard about trigonometry, you could use the properties of sine and cosine. For this special angle of 45°, both of them are equal to √2/2. So: To find the area of such triangle, use the basic triangle area formula is area = base * height / 2. In our case, one leg is a base and the other is the height, as there is a right angle between them. So the area of 45 45 90 triangles is: `area = a² / 2`To calculate the perimeter, simply add all 45 45 90 triangle sides: perimeter = a + b + c = a + a + a√2 = a(2 + √2)
The legs of such a triangle are equal, the hypotenuse is calculated immediately from the equation c = a√2. If the hypotenuse value is given, the side length will be equal to a = c√2/2. Triangles (set squares). The red one is the 45 45 90 degree angle triangle.
The most important rule is that this triangle has one right angle, and two other angles are equal to 45°. It implies that two sides - legs - are equal in length and the hypotenuse can be easily calculated. The other interesting properties of the 45 45 90 triangles are:
In a 45 45 90 triangle, the ratios are equal to:
Have a look at this real-life example to catch on the 45 45 90 triangle rules. Assume we want to solve the isosceles triangle from a triangle set.
Remember that every time you can change the units displayed by simply clicking on the unit name. Also, don't forget that our calculator is a flexible tool - if you only know the area, the hypotenuse or even the perimeter, it can calculate the remaining parameters as well. Awesome! |