Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 6   b = 27   c = 28

Area: T = 80.8610605365
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 12.35219946365° = 12°21'7″ = 0.21655829756 rad
Angle ∠ B = β = 74.2866138952° = 74°17'10″ = 1.29765377133 rad
Angle ∠ C = γ = 93.36218664115° = 93°21'43″ = 1.62994719647 rad

Height: ha = 26.95435351217
Height: hb = 5.99896744715
Height: hc = 5.77657575261

Median: ma = 27.3440446229
Median: mb = 15.09113882728
Median: mc = 13.65765002837

Inradius: r = 2.6511167389
Circumradius: R = 14.02441344333

Vertex coordinates: A[28; 0] B[0; 0] C[1.625; 5.77657575261]
Centroid: CG[9.875; 1.92552525087]
Coordinates of the circumscribed circle: U[14; -0.82224029452]
Coordinates of the inscribed circle: I[3.5; 2.6511167389]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.6488005363° = 167°38'53″ = 0.21655829756 rad
∠ B' = β' = 105.7143861048° = 105°42'50″ = 1.29765377133 rad
∠ C' = γ' = 86.63881335885° = 86°38'17″ = 1.62994719647 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 = 6+27+28 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-6)(30.5-27)(30.5-28) } ; ; T = sqrt{ 6538.44 } = 80.86 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 80.86 }{ 6 } = 26.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 80.86 }{ 27 } = 5.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 80.86 }{ 28 } = 5.78 ; ;

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{ 27**2+28**2-6**2 }{ 2 * 27 * 28 } ) = 12° 21'7" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6**2+28**2-27**2 }{ 2 * 6 * 28 } ) = 74° 17'10" ; ; gamma = 180° - alpha - beta = 180° - 12° 21'7" - 74° 17'10" = 93° 21'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 80.86 }{ 30.5 } = 2.65 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6 }{ 2 * sin 12° 21'7" } = 14.02 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 27**2+2 * 28**2 - 6**2 } }{ 2 } = 27.34 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 6**2 - 27**2 } }{ 2 } = 15.091 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 27**2+2 * 6**2 - 28**2 } }{ 2 } = 13.657 ; ;
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