Trigonometry calculator
In a right triangle an acute angle relates to the sides through three ratios: the sine is the opposite leg over the hypotenuse, the cosine is the adjacent leg over the hypotenuse, and the tangent is the opposite leg over the adjacent one. Any two known values are enough to find all the rest.
- Leg b
- 4
- Hypotenuse c
- 5
- Angle α
- 36.8699°
- Angle β
- 53.1301°
- Area
- 6
- Perimeter
- 12
Rates and thresholds
- Sine
- sin α = opposite / hypotenuse
- Cosine
- cos α = adjacent / hypotenuse
- Tangent
- tan α = opposite / adjacent
- Pythagorean theorem
- a² + b² = c²
- Sum of the acute angles
- α + β = 90°
How do you find an angle when you know the sides?
To get an angle from the sides you use the inverse functions: arcsine, arccosine and arctangent. If you know the opposite and adjacent legs, then α = arctan(opposite / adjacent). In a triangle with sides 3 and 4, for instance, α = arctan(3 / 4), about 36.87 degrees. On a calculator these are the sin⁻¹, cos⁻¹ and tan⁻¹ keys.
Degrees or radians — which should you use?
Estonian schools solve triangles in degrees, so that is the default here. Radians come up in higher mathematics and in programming: the trigonometric functions in almost every programming language expect radians. The conversion is 180 degrees = π radians, so degrees × π / 180 gives radians. The wrong mode is the most common source of errors — sin 30 is 0.5 in degrees but roughly −0.988 in radians.
Related calculators
- Percentage calculator
- Percentage change calculator
- Discount calculator
- Average calculator
- Circle calculator
- Triangle calculator