Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 12   b = 27   c = 30

Area: T = 161.8599313912
Perimeter: p = 69
Semiperimeter: s = 34.5

Angle ∠ A = α = 23.55664643091° = 23°33'23″ = 0.41111378623 rad
Angle ∠ B = β = 64.05655202276° = 64°3'20″ = 1.1187979732 rad
Angle ∠ C = γ = 92.38880154633° = 92°23'17″ = 1.61224750592 rad

Height: ha = 26.97765523186
Height: hb = 11.99895788083
Height: hc = 10.79106209275

Median: ma = 27.90216128566
Median: mb = 18.43223085912
Median: mc = 14.54330395722

Inradius: r = 4.69215743163
Circumradius: R = 15.01330378121

Vertex coordinates: A[30; 0] B[0; 0] C[5.25; 10.79106209275]
Centroid: CG[11.75; 3.59768736425]
Coordinates of the circumscribed circle: U[15; -0.62655432422]
Coordinates of the inscribed circle: I[7.5; 4.69215743163]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.4443535691° = 156°26'37″ = 0.41111378623 rad
∠ B' = β' = 115.9444479772° = 115°56'40″ = 1.1187979732 rad
∠ C' = γ' = 87.61219845367° = 87°36'43″ = 1.61224750592 rad

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How did we calculate this triangle?

a = 12 ; ; b = 27 ; ; c = 30 ; ;

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

p = a+b+c = 12+27+30 = 69 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 69 }{ 2 } = 34.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34.5 * (34.5-12)(34.5-27)(34.5-30) } ; ; T = sqrt{ 26198.44 } = 161.86 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 161.86 }{ 12 } = 26.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 161.86 }{ 27 } = 11.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 161.86 }{ 30 } = 10.79 ; ;

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+30**2-12**2 }{ 2 * 27 * 30 } ) = 23° 33'23" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 12**2+30**2-27**2 }{ 2 * 12 * 30 } ) = 64° 3'20" ; ; gamma = 180° - alpha - beta = 180° - 23° 33'23" - 64° 3'20" = 92° 23'17" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 161.86 }{ 34.5 } = 4.69 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 12 }{ 2 * sin 23° 33'23" } = 15.01 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 27**2+2 * 30**2 - 12**2 } }{ 2 } = 27.902 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 30**2+2 * 12**2 - 27**2 } }{ 2 } = 18.432 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 27**2+2 * 12**2 - 30**2 } }{ 2 } = 14.543 ; ;
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