Sheet metal
Right triangle calculator
In short
A right triangle is solved from two values, including at least one side. With a and b the sides of the right angle, c the hypotenuse and α the angle opposite a: c = √(a² + b²), a = c sin α = b tan α, b = c cos α, and β = 90° − α.
Calculation
Example calculated with the tool’s default values.
Inputs
- First known value
- Side a (opposite α)
- Value 1 (mm or °)
- 300
- Second known value
- Side b (opposite β)
- Value 2 (mm or °)
- 400
- Third value (leave on “None”)
- None
Results
- Hypotenuse c
- 500.00 mm
Worked example
Every value in this section belongs to the example, calculated with the tool’s default values.
Other results of the example
- Side a
- 300.00 mmGiven
- Side b
- 400.00 mmGiven
- Angle α
- 36.870°
- Angle β
- 53.130°
- Slope a / b
- 75.00%
- Area (a × b / 2)
- 60,000.0in mm²
- Perimeter
- 1200.00 mm
- Entered values and sides share the same unit (mm by default); only the right triangle is handled (right angle between a and b).
Step-by-step calculation
Given
right angle between a and b; α opposite a; β opposite b
a = 300.000 ; b = 400.000
Step 1
c = √(a² + b²)
√(300.00² + 400.00²) = 500.000
Step 2
α = atan(a / b)
atan(300.00 / 400.00) = 36.870°
Step 3
β = 90° − α
90 − 36.870 = 53.130°
Check
a² + b² = c²
90000.00 + 160000.00 = 250000.00 ; c² = 250000.00
How to use it
- Pick the first known value (side a, side b, hypotenuse c, angle α or angle β) and enter it.
- Pick and enter the second known value: at least one of the two must be a side.
- Leave the third value on "None": two values are enough.
- Read the hypotenuse c or, if it is given, the first unknown side.
Frequently asked questions
How do I find the hypotenuse of a right triangle?
From the two sides of the right angle, by Pythagoras: c = √(a² + b²). Example: a = 300 and b = 400 give c = √(300.00² + 400.00²) = 500.000. From a side and an angle: c = a / sin α, or c = b / cos α.
How do I solve a right triangle with angles?
With the angle α, opposite side a, and one side: if a is known, b = a / tan α and c = a / sin α; if b is known, a = b × tan α and c = b / cos α; if c is known, a = c × sin α and b = c × cos α. The other angle is β = 90° − α. Two angles alone are not enough: they give no length.
How do I find the angles from the sides?
α = atan(a / b), then β = 90° − α. Example: a = 300 and b = 400 give α = atan(300.00 / 400.00) = 36.870° and β = 90 − 36.870 = 53.130°. If the hypotenuse is known with one side, the other side is √(c² − a²) or √(c² − b²).
How do I find the missing sides of a right triangle?
b = √(c² − a²), or a = √(c² − b²). The hypotenuse must be strictly longer than the known side. The calculation also gives the slope a / b in %, the area a × b / 2 and the perimeter: for a = 300 and b = 400, slope 75 %, area 60000 mm², perimeter 1200 mm.
Limits
Indicative results. Only the right triangle is handled, with the right angle between a and b; entered values and sides share the same unit (mm by default). A third value makes the triangle over-determined: the calculation says so. Below 1°, the result is very sensitive to the precision of the data.
Sources
- Théorème de Pythagore et rapports trigonométriques du triangle rectangle : sin α = a / c ; cos α = b / c ; tan α = a / b (géométrie)