Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 22.24   b = 18.8   c = 36.44

Area: T = 171.2187548808
Perimeter: p = 77.48
Semiperimeter: s = 38.74

Angle ∠ A = α = 29.99902560311° = 29°59'25″ = 0.52334287113 rad
Angle ∠ B = β = 24.99548859087° = 24°59'42″ = 0.43662430553 rad
Angle ∠ C = γ = 125.015485806° = 125°53″ = 2.18219208871 rad

Height: ha = 15.39772615835
Height: hb = 18.2154632852
Height: hc = 9.39772309994

Median: ma = 26.77769004928
Median: mb = 28.68659826396
Median: mc = 9.59548110977

Inradius: r = 4.42196579455
Circumradius: R = 22.24765532681

Vertex coordinates: A[36.44; 0] B[0; 0] C[20.15771240395; 9.39772309994]
Centroid: CG[18.86657080132; 3.13224103331]
Coordinates of the circumscribed circle: U[18.22; -12.76548240219]
Coordinates of the inscribed circle: I[19.94; 4.42196579455]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.0109743969° = 150°35″ = 0.52334287113 rad
∠ B' = β' = 155.0055114091° = 155°18″ = 0.43662430553 rad
∠ C' = γ' = 54.98551419398° = 54°59'7″ = 2.18219208871 rad

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How did we calculate this triangle?

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 22.24+18.8+36.44 = 77.48 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 77.48 }{ 2 } = 38.74 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 38.74 * (38.74-22.24)(38.74-18.8)(38.74-36.44) } ; ; T = sqrt{ 29315.45 } = 171.22 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 171.22 }{ 22.24 } = 15.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 171.22 }{ 18.8 } = 18.21 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 171.22 }{ 36.44 } = 9.4 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos alpha ; ; alpha = arccos( fraction{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 18.8**2+36.44**2-22.24**2 }{ 2 * 18.8 * 36.44 } ) = 29° 59'25" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 22.24**2+36.44**2-18.8**2 }{ 2 * 22.24 * 36.44 } ) = 24° 59'42" ; ;
 gamma = 180° - alpha - beta = 180° - 29° 59'25" - 24° 59'42" = 125° 53" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 171.22 }{ 38.74 } = 4.42 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 22.24 }{ 2 * sin 29° 59'25" } = 22.25 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 18.8**2+2 * 36.44**2 - 22.24**2 } }{ 2 } = 26.777 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 36.44**2+2 * 22.24**2 - 18.8**2 } }{ 2 } = 28.686 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 18.8**2+2 * 22.24**2 - 36.44**2 } }{ 2 } = 9.595 ; ;
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