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Triangle Calculator
Make calculations in an arbitrary triangle. Enter three values, including at least one side length. Please enter angles in degrees, here you can convert angle units.Triangle shape:
Formulas:
SSS: Law of cosines: α = arccos( (b² + c² - a²) / 2bc ), β = arccos( (a² + c² - b²) / 2ac ), γ = arccos( (a² + b² - c²) / 2ab )
SAS: a = √ ( b² + c² ) - 2bc * cos( α )), b = √ ( a² + c² ) - 2ac * cos( β )), c = √ ( a² + b² ) - 2ab * cos( γ ))
SSA: Law of sines: a / sin( α ) = b / sin( β ) = c / sin( γ )
unique, if the known angular is opposite to the larger of the two given sides, otherwise there are two solutions.
ASA and AAS: Third angle = 180° - other two angles, then law of sines
p = a + b + c, A = √p/2 * (p/2-a) * (p/2-b) * (p/2-c)
Heights: ha = c * sin( β ), hb = a * sin( γ ), hc = b * sin( α )
r = a / (2 * sin( α/2 )), ρ = 4r * sin( α/2 ) * sin( β/2 ) * sin( γ/2 )
SSS: Law of cosines: α = arccos( (b² + c² - a²) / 2bc ), β = arccos( (a² + c² - b²) / 2ac ), γ = arccos( (a² + b² - c²) / 2ab )
SAS: a = √ ( b² + c² ) - 2bc * cos( α )), b = √ ( a² + c² ) - 2ac * cos( β )), c = √ ( a² + b² ) - 2ab * cos( γ ))
SSA: Law of sines: a / sin( α ) = b / sin( β ) = c / sin( γ )
unique, if the known angular is opposite to the larger of the two given sides, otherwise there are two solutions.
ASA and AAS: Third angle = 180° - other two angles, then law of sines
p = a + b + c, A = √p/2 * (p/2-a) * (p/2-b) * (p/2-c)
Heights: ha = c * sin( β ), hb = a * sin( γ ), hc = b * sin( α )
r = a / (2 * sin( α/2 )), ρ = 4r * sin( α/2 ) * sin( β/2 ) * sin( γ/2 )
Side length, perimeter, radius and heights have the same unit (e.g. meter), the area has this unit squared (e.g. square meter), the angles are in degrees.
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