Online Right Triangle Trigonometry Calculator
Solve right triangles instantly with two given values: find missing side lengths, hypotenuse, angles, area, and perimeter using Pythagorean theorem and trigonometric functions.
Trigonometric Ratios (α = 36.87°, β = 53.13°)
| Функція | Кут α (36.9°) | Кут β (53.1°) | Співвідношення сторін |
|---|---|---|---|
| sin (Синус) | 0.6 | 0.8 | протилежний / гіпотенуза |
| cos (Косинус) | 0.8 | 0.6 | прилеглий / гіпотенуза |
| tan (Тангенс) | 0.75 | 1.3333 | протилежний / прилеглий |
| cot (Котангенс) | 1.3333 | 0.75 | прилеглий / протилежний |
| sec (Секанс) | 1.25 | 1.6667 | 1 / cos |
| csc (Косеканс) | 1.6667 | 1.25 | 1 / sin |
How to use
- Input any two known values (legs a and b, leg and hypotenuse, or side and acute angle).
- Click calculate.
- View complete triangle geometry: hypotenuse, angles, perimeter, and surface area.
Trigonometric & Geometry Principles
Pythagorean theorem: c² = a² + b² (where c is hypotenuse, a and b are legs).
Sine ratio: sin(α) = a / c (opposite leg / hypotenuse).
Cosine ratio: cos(α) = b / c (adjacent leg / hypotenuse).
Tangent ratio: tan(α) = a / b (opposite leg / adjacent leg).
Area: S = (a * b) / 2.
Calculation Methodology
A right-angled triangle contains one 90° right angle; complementary acute angles sum up to 90° (α + β = 90°).
Frequently Asked Questions
How many inputs are required to solve a right triangle?
Exactly two known values are required, with at least one being a side length.
How to find hypotenuse length from legs?
Apply the Pythagorean theorem: c = √(a² + b²).
What is the sum of angles in a right triangle?
All triangle interior angles sum to 180° (90° right angle + two complementary acute angles summing to 90°).
How is right triangle area evaluated?
Area is half the product of perpendicular legs: Area = 1/2 * a * b.
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