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Online Right Triangle Calculator
Calculate sides, angles, area, and perimeter of right triangles accurately using trigonometric identities and the Pythagorean theorem. Ideal for students, engineers, and professionals.
| Result | |||
|---|---|---|---|
| a | 3 | ||
| b | 4 | ||
| c | 5 | ||
| h | 2.4 | ||
| α | 36.8699° = 0.6435011 rad | ||
| β | 53.1301° = 0.9272952 rad | ||
| S (area) | 6 | inradius | 1 |
| p (perimeter) | 12 | circumradius | 2.5 |
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What Is This Tool?
This calculator helps you find unknown sides or angles of a right triangle by applying the Pythagorean theorem and trigonometric ratios. Simply input at least two known values, and it computes the remaining measurements with high precision.
How to Use This Tool?
- Enter known values of at least two sides or one side and an angle.
- Select the corresponding variables (a, b, c, A, or B) for your inputs.
- Click the calculate button to get missing side lengths, angles, area, and perimeter.
- Review results displayed with appropriate units and decimal precision.
- Use outputs for your geometry, engineering, or construction needs.
Key Features
- Calculates missing side lengths using the Pythagorean theorem.
- Finds angles using sine, cosine, and tangent ratios and their inverses.
- Computes triangle area and perimeter based on input sides.
- Supports high-precision calculations for accurate results.
- User-friendly interface for quick and easy inputs.
Examples
- Given legs a = 9 and b = 12, the hypotenuse c is calculated as 15 by applying \(c = \sqrt{9^2 + 12^2}\).
- Angle A opposite side a can be found using inverse tangent: \(A = \arctan(9/12) \approx 36.87^\circ\).
- Area of the triangle with legs 9 and 12 is calculated as \(\frac{1}{2} \times 9 \times 12 = 54\).
Common Use Cases
- Students learning geometry and trigonometry concepts.
- Teachers preparing lessons and problem solutions.
- Architects and engineers designing right-angle structures.
- Carpenters and surveyors calculating dimensions for construction.
- Anyone needing quick and reliable right triangle measurements.
Tips & Best Practices
- Always ensure you input at least two known values from sides or angles.
- Double-check unit consistency before entering dimensions.
- Use the calculator to verify manual computations for accuracy.
- Input values carefully to avoid invalid or impossible triangle configurations.
- Familiarize yourself with the Pythagorean theorem and trigonometric basics for better understanding.
Limitations
- Only valid for right triangles with one 90° angle.
- Cannot solve triangles that are non-right angled or have invalid side lengths.
- Requires at least two known values to compute unknown sides or angles.
- Not suitable for obtuse or acute triangles without a right angle.
Frequently Asked Questions
- Can this calculator find angles if only sides are known?
- Yes, by using inverse trigonometric functions such as arcsin, arccos, and arctan, the calculator can find angles when side lengths are provided.
- Is it possible to calculate area and perimeter with this tool?
- Absolutely. Once side lengths are known, the calculator computes area using \(\frac{1}{2}ab\) and perimeter by summing all sides.
- Does the calculator work for any triangle shape?
- No, it is designed exclusively for right triangles which have one 90° angle.
Key Terminology
- Hypotenuse
- The longest side of a right triangle, opposite the right angle, denoted as \(c\).
- Adjacent Side
- The side next to a given angle in a triangle that is not the hypotenuse.
- Opposite Side
- The side directly opposite a given angle in a triangle.
- Pythagorean Theorem
- A formula that relates the sides of a right triangle as \(a^2 + b^2 = c^2\).
- Trigonometric Ratios
- Relationships between the angles and sides of a right triangle involving sine, cosine, and tangent.