Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 18.76   b = 16.15   c = 3.35

Area: T = 18.24439964273
Perimeter: p = 38.26
Semiperimeter: s = 19.13

Angle ∠ A = α = 137.5910608875° = 137°35'26″ = 2.40114091447 rad
Angle ∠ B = β = 35.49223125015° = 35°29'32″ = 0.61994577123 rad
Angle ∠ C = γ = 6.91770786235° = 6°55'1″ = 0.12107257966 rad

Height: ha = 1.94549889581
Height: hb = 2.2599318443
Height: hc = 10.89219381656

Median: ma = 6.93109523155
Median: mb = 10.78876978545
Median: mc = 17.42333872998

Inradius: r = 0.95436851243
Circumradius: R = 13.90881766438

Vertex coordinates: A[3.35; 0] B[0; 0] C[15.27442686567; 10.89219381656]
Centroid: CG[6.20880895522; 3.63106460552]
Coordinates of the circumscribed circle: U[1.675; 13.80769458084]
Coordinates of the inscribed circle: I[2.98; 0.95436851243]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 42.4099391125° = 42°24'34″ = 2.40114091447 rad
∠ B' = β' = 144.5087687499° = 144°30'28″ = 0.61994577123 rad
∠ C' = γ' = 173.0832921377° = 173°4'59″ = 0.12107257966 rad

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How did we calculate this triangle?

a = 18.76 ; ; b = 16.15 ; ; c = 3.35 ; ;

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

p = a+b+c = 18.76+16.15+3.35 = 38.26 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 38.26 }{ 2 } = 19.13 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19.13 * (19.13-18.76)(19.13-16.15)(19.13-3.35) } ; ; T = sqrt{ 332.84 } = 18.24 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 18.24 }{ 18.76 } = 1.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 18.24 }{ 16.15 } = 2.26 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 18.24 }{ 3.35 } = 10.89 ; ;

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{ 16.15**2+3.35**2-18.76**2 }{ 2 * 16.15 * 3.35 } ) = 137° 35'26" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 18.76**2+3.35**2-16.15**2 }{ 2 * 18.76 * 3.35 } ) = 35° 29'32" ; ; gamma = 180° - alpha - beta = 180° - 137° 35'26" - 35° 29'32" = 6° 55'1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 18.24 }{ 19.13 } = 0.95 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 18.76 }{ 2 * sin 137° 35'26" } = 13.91 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 16.15**2+2 * 3.35**2 - 18.76**2 } }{ 2 } = 6.931 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.35**2+2 * 18.76**2 - 16.15**2 } }{ 2 } = 10.788 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 16.15**2+2 * 18.76**2 - 3.35**2 } }{ 2 } = 17.423 ; ;
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