Right Triangle Calculator
Right Triangle Calculator
The Right Triangle Calculator helps you find missing values of a right-angled triangle using known side lengths or angles. It can calculate sides, angles, height, area, and perimeter based on the given inputs.
What is a Right Triangle?
A right triangle is a triangle that contains one angle equal to 90°. It is one of the most important shapes in trigonometry and geometry because its properties are used in many mathematical applications.
- One angle is always 90°
- The longest side is called the hypotenuse
- Used in trigonometry and Pythagorean theorem
Right Triangle Labels
- a and b: the two perpendicular sides
- c: the hypotenuse (longest side)
- α (alpha) and β (beta): the two acute angles
- h: height from right angle to hypotenuse
Pythagorean Theorem
The Pythagorean theorem is the fundamental rule for right triangles:
a² + b² = c²
Area of a Right Triangle
The area is calculated using the formula:
A = 1/2 × a × b
Perimeter of a Right Triangle
The perimeter is the sum of all three sides:
P = a + b + c
Given Values Example
- a = 3
- c = 5
- b = unknown
- Angles = α and β
How to Solve a Right Triangle
- Use Pythagorean theorem to find missing side
- Use trigonometric ratios for angles
- Use area formula once two sides are known
Special Right Triangles
30°-60°-90° Triangle
This triangle follows a fixed ratio:
1 : √3 : 2
45°-45°-90° Triangle
This triangle follows the ratio:
1 : 1 : √2
Applications of Right Triangles
- Engineering and construction
- Navigation and GPS systems
- Architecture design
- Physics and force calculations
- Computer graphics and animation
FAQs
What is a right triangle?
A triangle with one angle equal to 90 degrees.
What is the hypotenuse?
The longest side opposite the right angle.
What is the Pythagorean theorem?
a² + b² = c², used to find missing sides of a right triangle.
How is area calculated?
A = 1/2 × a × b
References
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