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. Hence, the length of the other side is 5 units each.- Side A, Side B, or Side C: Enter the length of any two sides of the right triangle. Ques: Find the length of the other two sides of the isosceles right triangle given below: (2 marks)Īns: We know the length of the hypotenuse is \(\sqrt\) units In the right isosceles triangle, since two sides (Base BC and Height AB) are same and taken as ‘B’ each. The Sum of all sides of a triangle is the perimeter of that triangle. If, base (BC) is taken as ‘B’, then AB=BC=’B’ This applies to right isosceles triangles also.Īs stated above, in an isosceles right-triangle the length of base (BC) is equal to length of height (AB). The area of a triangle is half of the base times height. Pythagoras theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the square of the other two sides. If base (BC) is taken as ‘B’, then AB=BC=’B’. In an isosceles right triangle, the length of base (BC) is equal to length of height (AB). Pythagoras theorem, which applies to any right-angle triangle, also applies to isosceles right triangles. Given below are the formulas to construct a triangle which includes: And AB or AC can be taken as height or base This type of triangle is also known as a 45-90-45 triangleĪC, the side opposite of ∠B, is the hypotenuse. In an isosceles right triangle (figure below), ∠A and ∠C measure 45° each, and ∠B measures 90°. A triangle in which one angle measures 90°, and the other two angles measure 45° each is an isosceles right triangle.
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