Right Triangle Calculator
The right triangle calculator allows you to calculate the basic parameters of a triangle, such as side lengths, area and perimeter, knowing some of them.
Enter only what you know:
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The right triangle calculator allows you to calculate all the elements of a triangle. It is enough to specify any two values and the calculator will calculate in various ways all the missing angles, sides, medians, heights and radii of the inscribed and circumscribed circle. In addition to the calculation, it calculates the perimeter and area of the triangle.
A right triangle is a triangle in which one of the angles is equal to 90 degrees.
The main characteristics of a right triangle
1. Angles:
• One angle is equal to 90° (a right angle).
• The other two angles are always acute and add up to 90° (since the sum of the angles in any triangle is equal to 180°).
2. Sides:
• Legs: the two sides that form a right angle (denoted as a and b ).
• Hypotenuse: the side opposite the right angle is the longest side (denoted as c ).
3. Pythagoras' Theorem:
• The main property of a right triangle: the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.
• Formula: c² = a² + b² .
Parameters
1. Area:
• The area S of a right triangle is calculated by the formula: S = a ⋅ b / 2
2. Perimeter:
• The perimeter P of a right triangle is calculated by the formula: P = a + b + c
Application
• Right triangles are widely used in geometry, trigonometry, architecture and engineering.
• They are the basis for defining trigonometric functions (sine, cosine, tangent).
Trigonometry
• In a right triangle, the trigonometric functions are defined as follows:
• Sine of angle α (opposite leg to hypotenuse):
sin(α) = a / c
• Cosine of angle α (adjacent leg to hypotenuse):
cos(α) = b / c
• Tangent of angle α (opposite leg to adjacent):
tan(α) = a / b
Right triangles play an important role in mathematics and related fields. Their properties and theorems allow us to solve many problems related to geometry and physics.
The main characteristics of a right triangle
1. Angles:
• One angle is equal to 90° (a right angle).
• The other two angles are always acute and add up to 90° (since the sum of the angles in any triangle is equal to 180°).
2. Sides:
• Legs: the two sides that form a right angle (denoted as a and b ).
• Hypotenuse: the side opposite the right angle is the longest side (denoted as c ).
3. Pythagoras' Theorem:
• The main property of a right triangle: the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.
• Formula: c² = a² + b² .
Parameters
1. Area:
• The area S of a right triangle is calculated by the formula: S = a ⋅ b / 2
2. Perimeter:
• The perimeter P of a right triangle is calculated by the formula: P = a + b + c
Application
• Right triangles are widely used in geometry, trigonometry, architecture and engineering.
• They are the basis for defining trigonometric functions (sine, cosine, tangent).
Trigonometry
• In a right triangle, the trigonometric functions are defined as follows:
• Sine of angle α (opposite leg to hypotenuse):
sin(α) = a / c
• Cosine of angle α (adjacent leg to hypotenuse):
cos(α) = b / c
• Tangent of angle α (opposite leg to adjacent):
tan(α) = a / b
Right triangles play an important role in mathematics and related fields. Their properties and theorems allow us to solve many problems related to geometry and physics.