Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 16.51   b = 15.25   c = 27.85

Area: T = 106.1866234313
Perimeter: p = 59.61
Semiperimeter: s = 29.805

Angle ∠ A = α = 30.00325264839° = 30°9″ = 0.52436428711 rad
Angle ∠ B = β = 27.50882663054° = 27°30'30″ = 0.48801098185 rad
Angle ∠ C = γ = 122.4899207211° = 122°29'21″ = 2.1387839964 rad

Height: ha = 12.86332627878
Height: hb = 13.92660635165
Height: hc = 7.62655823564

Median: ma = 20.87993552343
Median: mb = 21.5866122278
Median: mc = 7.65993521266

Inradius: r = 3.56326986852
Circumradius: R = 16.50987391515

Vertex coordinates: A[27.85; 0] B[0; 0] C[14.6433448833; 7.62655823564]
Centroid: CG[14.16444829443; 2.54218607855]
Coordinates of the circumscribed circle: U[13.925; -8.86875161895]
Coordinates of the inscribed circle: I[14.555; 3.56326986852]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.9977473516° = 149°59'51″ = 0.52436428711 rad
∠ B' = β' = 152.4921733695° = 152°29'30″ = 0.48801098185 rad
∠ C' = γ' = 57.51107927893° = 57°30'39″ = 2.1387839964 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 = 16.51+15.25+27.85 = 59.61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59.61 }{ 2 } = 29.81 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.81 * (29.81-16.51)(29.81-15.25)(29.81-27.85) } ; ; T = sqrt{ 11275.52 } = 106.19 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 106.19 }{ 16.51 } = 12.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 106.19 }{ 15.25 } = 13.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 106.19 }{ 27.85 } = 7.63 ; ;

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{ 15.25**2+27.85**2-16.51**2 }{ 2 * 15.25 * 27.85 } ) = 30° 9" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 16.51**2+27.85**2-15.25**2 }{ 2 * 16.51 * 27.85 } ) = 27° 30'30" ; ; gamma = 180° - alpha - beta = 180° - 30° 9" - 27° 30'30" = 122° 29'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 106.19 }{ 29.81 } = 3.56 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 16.51 }{ 2 * sin 30° 9" } = 16.51 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 15.25**2+2 * 27.85**2 - 16.51**2 } }{ 2 } = 20.879 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 27.85**2+2 * 16.51**2 - 15.25**2 } }{ 2 } = 21.586 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 15.25**2+2 * 16.51**2 - 27.85**2 } }{ 2 } = 7.659 ; ;
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