Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 9.63   b = 22   c = 22.43

Area: T = 104.3188313042
Perimeter: p = 54.06
Semiperimeter: s = 27.03

Angle ∠ A = α = 25.01217125229° = 25°42″ = 0.43765367351 rad
Angle ∠ B = β = 74.99656738676° = 74°59'44″ = 1.30989214337 rad
Angle ∠ C = γ = 79.99326136094° = 79°59'33″ = 1.39661344848 rad

Height: ha = 21.66552778904
Height: hb = 9.48334830038
Height: hc = 9.30216774893

Median: ma = 21.68879742023
Median: mb = 13.30111616034
Median: mc = 12.7511165633

Inradius: r = 3.85993530537
Circumradius: R = 11.38882684195

Vertex coordinates: A[22.43; 0] B[0; 0] C[2.4933129737; 9.30216774893]
Centroid: CG[8.30877099123; 3.10105591631]
Coordinates of the circumscribed circle: U[11.215; 1.97989978766]
Coordinates of the inscribed circle: I[5.03; 3.85993530537]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.9888287477° = 154°59'18″ = 0.43765367351 rad
∠ B' = β' = 105.0044326132° = 105°16″ = 1.30989214337 rad
∠ C' = γ' = 100.0077386391° = 100°27″ = 1.39661344848 rad

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How did we calculate this triangle?

a = 9.63 ; ; b = 22 ; ; c = 22.43 ; ;

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

p = a+b+c = 9.63+22+22.43 = 54.06 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 54.06 }{ 2 } = 27.03 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.03 * (27.03-9.63)(27.03-22)(27.03-22.43) } ; ; T = sqrt{ 10882.31 } = 104.32 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 104.32 }{ 9.63 } = 21.67 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 104.32 }{ 22 } = 9.48 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 104.32 }{ 22.43 } = 9.3 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 9.63**2-22**2-22.43**2 }{ 2 * 22 * 22.43 } ) = 25° 42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-9.63**2-22.43**2 }{ 2 * 9.63 * 22.43 } ) = 74° 59'44" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22.43**2-9.63**2-22**2 }{ 2 * 22 * 9.63 } ) = 79° 59'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 104.32 }{ 27.03 } = 3.86 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9.63 }{ 2 * sin 25° 42" } = 11.39 ; ;

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