Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 24.69   b = 66.69   c = 57.44

Area: T = 696.1954813531
Perimeter: p = 148.82
Semiperimeter: s = 74.41

Angle ∠ A = α = 21.31443323027° = 21°18'52″ = 0.37220052765 rad
Angle ∠ B = β = 100.9466464266° = 100°56'47″ = 1.76218481697 rad
Angle ∠ C = γ = 57.73992034312° = 57°44'21″ = 1.00877392074 rad

Height: ha = 56.39548816145
Height: hb = 20.8798536918
Height: hc = 24.24107664879

Median: ma = 611.0004575803
Median: mb = 29.02773289333
Median: mc = 41.27663576397

Inradius: r = 9.35661996174
Circumradius: R = 33.963295453

Vertex coordinates: A[57.44; 0] B[0; 0] C[-4.68884261838; 24.24107664879]
Centroid: CG[17.58438579387; 8.0880255496]
Coordinates of the circumscribed circle: U[28.72; 18.1298537735]
Coordinates of the inscribed circle: I[7.72; 9.35661996174]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.6865667697° = 158°41'8″ = 0.37220052765 rad
∠ B' = β' = 79.05435357339° = 79°3'13″ = 1.76218481697 rad
∠ C' = γ' = 122.2610796569° = 122°15'39″ = 1.00877392074 rad

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How did we calculate this triangle?

a = 24.69 ; ; b = 66.69 ; ; c = 57.44 ; ;

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

p = a+b+c = 24.69+66.69+57.44 = 148.82 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 148.82 }{ 2 } = 74.41 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 74.41 * (74.41-24.69)(74.41-66.69)(74.41-57.44) } ; ; T = sqrt{ 484687.22 } = 696.19 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 696.19 }{ 24.69 } = 56.39 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 696.19 }{ 66.69 } = 20.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 696.19 }{ 57.44 } = 24.24 ; ;

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{ 66.69**2+57.44**2-24.69**2 }{ 2 * 66.69 * 57.44 } ) = 21° 18'52" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 24.69**2+57.44**2-66.69**2 }{ 2 * 24.69 * 57.44 } ) = 100° 56'47" ; ; gamma = 180° - alpha - beta = 180° - 21° 18'52" - 100° 56'47" = 57° 44'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 696.19 }{ 74.41 } = 9.36 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 24.69 }{ 2 * sin 21° 18'52" } = 33.96 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 66.69**2+2 * 57.44**2 - 24.69**2 } }{ 2 } = 61 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 57.44**2+2 * 24.69**2 - 66.69**2 } }{ 2 } = 29.027 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 66.69**2+2 * 24.69**2 - 57.44**2 } }{ 2 } = 41.276 ; ;
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