Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 33   b = 32   c = 2.45

Area: T = 36.31993603621
Perimeter: p = 67.45
Semiperimeter: s = 33.725

Angle ∠ A = α = 112.1022183137° = 112°6'8″ = 1.95765521944 rad
Angle ∠ B = β = 63.95435164775° = 63°57'13″ = 1.11661994308 rad
Angle ∠ C = γ = 3.94443003852° = 3°56'39″ = 0.06988410284 rad

Height: ha = 2.20111733553
Height: hb = 2.27699600226
Height: hc = 29.64884574384

Median: ma = 15.58804765652
Median: mb = 17.07334076856
Median: mc = 32.48107539167

Inradius: r = 1.07769269196
Circumradius: R = 17.80986836759

Vertex coordinates: A[2.45; 0] B[0; 0] C[14.49903061224; 29.64884574384]
Centroid: CG[5.64767687075; 9.88328191461]
Coordinates of the circumscribed circle: U[1.225; 17.76765018861]
Coordinates of the inscribed circle: I[1.725; 1.07769269196]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 67.89878168626° = 67°53'52″ = 1.95765521944 rad
∠ B' = β' = 116.0466483523° = 116°2'47″ = 1.11661994308 rad
∠ C' = γ' = 176.0565699615° = 176°3'21″ = 0.06988410284 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 = 33+32+2.45 = 67.45 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67.45 }{ 2 } = 33.73 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.73 * (33.73-33)(33.73-32)(33.73-2.45) } ; ; T = sqrt{ 1319.1 } = 36.32 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 36.32 }{ 33 } = 2.2 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 36.32 }{ 32 } = 2.27 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 36.32 }{ 2.45 } = 29.65 ; ;

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{ 32**2+2.45**2-33**2 }{ 2 * 32 * 2.45 } ) = 112° 6'8" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 33**2+2.45**2-32**2 }{ 2 * 33 * 2.45 } ) = 63° 57'13" ; ;
 gamma = 180° - alpha - beta = 180° - 112° 6'8" - 63° 57'13" = 3° 56'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 36.32 }{ 33.73 } = 1.08 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 33 }{ 2 * sin 112° 6'8" } = 17.81 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 32**2+2 * 2.45**2 - 33**2 } }{ 2 } = 15.58 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.45**2+2 * 33**2 - 32**2 } }{ 2 } = 17.073 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 32**2+2 * 33**2 - 2.45**2 } }{ 2 } = 32.481 ; ;
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