Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 11   b = 23   c = 30

Area: T = 109.9821816679
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 18.59896365026° = 18°35'23″ = 0.32444503637 rad
Angle ∠ B = β = 41.80218441931° = 41°48'7″ = 0.73295798146 rad
Angle ∠ C = γ = 119.6098519304° = 119°36'31″ = 2.08875624753 rad

Height: ha = 19.99766939416
Height: hb = 9.5643636233
Height: hc = 7.33221211119

Median: ma = 26.15881727191
Median: mb = 19.44986503388
Median: mc = 10

Inradius: r = 3.43769317712
Circumradius: R = 17.25328519468

Vertex coordinates: A[30; 0] B[0; 0] C[8.2; 7.33221211119]
Centroid: CG[12.73333333333; 2.44440403706]
Coordinates of the circumscribed circle: U[15; -8.52441363373]
Coordinates of the inscribed circle: I[9; 3.43769317712]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.4110363497° = 161°24'37″ = 0.32444503637 rad
∠ B' = β' = 138.1988155807° = 138°11'53″ = 0.73295798146 rad
∠ C' = γ' = 60.39114806958° = 60°23'29″ = 2.08875624753 rad

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How did we calculate this triangle?

a = 11 ; ; b = 23 ; ; c = 30 ; ;

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

p = a+b+c = 11+23+30 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-11)(32-23)(32-30) } ; ; T = sqrt{ 12096 } = 109.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 109.98 }{ 11 } = 20 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 109.98 }{ 23 } = 9.56 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 109.98 }{ 30 } = 7.33 ; ;

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{ 23**2+30**2-11**2 }{ 2 * 23 * 30 } ) = 18° 35'23" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 11**2+30**2-23**2 }{ 2 * 11 * 30 } ) = 41° 48'7" ; ; gamma = 180° - alpha - beta = 180° - 18° 35'23" - 41° 48'7" = 119° 36'31" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 109.98 }{ 32 } = 3.44 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 11 }{ 2 * sin 18° 35'23" } = 17.25 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 23**2+2 * 30**2 - 11**2 } }{ 2 } = 26.158 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 30**2+2 * 11**2 - 23**2 } }{ 2 } = 19.449 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 23**2+2 * 11**2 - 30**2 } }{ 2 } = 10 ; ;
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