Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 14.32   b = 7.07   c = 18.03

Area: T = 47.49769664177
Perimeter: p = 39.42
Semiperimeter: s = 19.71

Angle ∠ A = α = 48.17774422892° = 48°10'39″ = 0.84108549931 rad
Angle ∠ B = β = 21.5887589914° = 21°35'15″ = 0.37767745216 rad
Angle ∠ C = γ = 110.2354967797° = 110°14'6″ = 1.92439631389 rad

Height: ha = 6.63436545276
Height: hb = 13.43661998353
Height: hc = 5.26986596137

Median: ma = 11.6733358557
Median: mb = 15.89326217158
Median: mc = 6.80109870607

Inradius: r = 2.41097902799
Circumradius: R = 9.60879845182

Vertex coordinates: A[18.03; 0] B[0; 0] C[13.31655407654; 5.26986596137]
Centroid: CG[10.44985135885; 1.75662198712]
Coordinates of the circumscribed circle: U[9.015; -3.32331222519]
Coordinates of the inscribed circle: I[12.64; 2.41097902799]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 131.8232557711° = 131°49'21″ = 0.84108549931 rad
∠ B' = β' = 158.4122410086° = 158°24'45″ = 0.37767745216 rad
∠ C' = γ' = 69.76550322032° = 69°45'54″ = 1.92439631389 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 = 14.32+7.07+18.03 = 39.42 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 39.42 }{ 2 } = 19.71 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19.71 * (19.71-14.32)(19.71-7.07)(19.71-18.03) } ; ; T = sqrt{ 2255.96 } = 47.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 47.5 }{ 14.32 } = 6.63 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 47.5 }{ 7.07 } = 13.44 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 47.5 }{ 18.03 } = 5.27 ; ;

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{ 7.07**2+18.03**2-14.32**2 }{ 2 * 7.07 * 18.03 } ) = 48° 10'39" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 14.32**2+18.03**2-7.07**2 }{ 2 * 14.32 * 18.03 } ) = 21° 35'15" ; ; gamma = 180° - alpha - beta = 180° - 48° 10'39" - 21° 35'15" = 110° 14'6" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 47.5 }{ 19.71 } = 2.41 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 14.32 }{ 2 * sin 48° 10'39" } = 9.61 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.07**2+2 * 18.03**2 - 14.32**2 } }{ 2 } = 11.673 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 18.03**2+2 * 14.32**2 - 7.07**2 } }{ 2 } = 15.893 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.07**2+2 * 14.32**2 - 18.03**2 } }{ 2 } = 6.801 ; ;
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