The angles are 45 degrees, 45 degrees, and 90 degrees.As you know one leg length a, you the know the length of the other as well, as both of them are equal.įind the hypotenuse from the Pythagorean theorem: we have a² + b² = c² and a = b, soĭid you notice that the 45 45 90 triangle is half of a square, cut along the square's diagonal? The length of the hypotenuse is equal to √2 times the length of either leg. This triangle is also known as an isosceles right triangle. In a 45-45-90 triangle, the two legs are congruent (equal in length) and the angles are 45 degrees, 45 degrees, and 90 degrees. These special right triangles are the 45-45-90 triangle and the 30-60-90 triangle. In addition to the general properties of right triangles, there are two special types of right triangles that have distinct characteristics and can be easily recognized based on their side lengths and angles. They are particularly useful for solving problems involving distances, angles of elevation and depression, and trigonometric functions. Right triangles have various applications in mathematics, physics, and engineering. The area of a right triangle can be calculated using the formula: Area = (1/2) * base * height, where the base and height are the lengths of the legs. ![]() The lengths of the legs and the hypotenuse are related by the Pythagorean theorem. In a right triangle, since one angle is fixed at 90 degrees, the sum of the other two angles is always 90 degrees. The sum of the interior angles of any triangle is always 180 degrees. Right triangles have several important properties and relationships. So, in this example, the hypotenuse (Side C) of the right triangle measures 5 units. Taking the square root of both sides, we find: Mathematically, it can be written as:įor example, let's consider a right triangle with side lengths of a = 3 units and b = 4 units. It states that the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the two legs (a and b). The Pythagorean theorem is a fundamental formula that relates the lengths of the sides of a right triangle. Acute Angles (∠A and ∠B): The two smaller angles of the right triangle that are less than 90 degrees. Right Angle (∠C): The angle that measures 90 degrees and is formed between the hypotenuse and one of the legs. These sides are adjacent to the right angle. Legs (Side A and Side B): The two shorter sides that form the right angle. Hypotenuse (Side C): The longest side of the right triangle and is always opposite the right angle. Let's break down the key concepts of a right triangle: This right angle is formed when one of the sides is perpendicular to the other side, creating a perfect L-shape. ![]() It is called a "right" triangle because it contains one right angle, which measures exactly 90 degrees (90°). What is a Right Triangle?Ī right triangle is a fundamental geometric shape that consists of three sides and three angles. Use the Right Triangle Calculator to explore various configurations and properties of right triangles quickly and accurately. The calculator will also provide a visual representation of the right triangle with labeled sides and angles. Enter the value "4" for Side A and "30" for ∠β. Suppose you know Side A = 4 units and ∠β = 30 degrees.ġ. Note: If any input was not provided, the calculator will automatically calculate it based on the other available values. Circumradius: The radius of the circumscribed circle around the triangle. Inradius: The radius of the inscribed circle within the triangle. Perimeter: The total length of all three sides. Area: The area of the triangle based on the given inputs. ![]() Height (h): If not provided, it will be calculated based on the other inputs. ∠α (Alpha) and ∠β (Beta): The calculated angles in degrees. ![]() Side A, Side B, and Side C: These values represent the lengths of the triangle sides. Click the "Calculate" button to perform the calculations. Note: At least two valid inputs are required for the calculations to work.Ģ. Perimeter: Similarly, if you know the perimeter of the triangle, you can input it. Area: If you know the area of the triangle, you can enter its value. Height (h): Optionally, you can provide the height of the triangle perpendicular to the base. The other angle will be calculated as 90 degrees minus the specified angle. ∠α (Alpha) or ∠β (Beta): Enter the value of either angle in degrees. The third side will be automatically calculated using the Pythagorean theorem. Side A, Side B, or Side C: Enter the length of any two sides of the right triangle.
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