Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 42   b = 33   c = 42.45

Area: T = 641.2587955847
Perimeter: p = 117.45
Semiperimeter: s = 58.725

Angle ∠ A = α = 66.28106704526° = 66°16'50″ = 1.15768159298 rad
Angle ∠ B = β = 466.0002304625° = 46°1″ = 0.80328554782 rad
Angle ∠ C = γ = 67.71990990849° = 67°43'9″ = 1.18219212455 rad

Height: ha = 30.53660931356
Height: hb = 38.86441185362
Height: hc = 30.21223889681

Median: ma = 31.69438677034
Median: mb = 38.86883836813
Median: mc = 31.24109887007

Inradius: r = 10.92196757062
Circumradius: R = 22.9387610155

Vertex coordinates: A[42.45; 0] B[0; 0] C[29.17655300353; 30.21223889681]
Centroid: CG[23.87551766784; 10.07107963227]
Coordinates of the circumscribed circle: U[21.225; 8.69767427593]
Coordinates of the inscribed circle: I[25.725; 10.92196757062]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 113.7199329547° = 113°43'10″ = 1.15768159298 rad
∠ B' = β' = 1343.999769538° = 133°59'59″ = 0.80328554782 rad
∠ C' = γ' = 112.2810900915° = 112°16'51″ = 1.18219212455 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 = 42+33+42.45 = 117.45 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 117.45 }{ 2 } = 58.73 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 58.73 * (58.73-42)(58.73-33)(58.73-42.45) } ; ; T = sqrt{ 411211.77 } = 641.26 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 641.26 }{ 42 } = 30.54 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 641.26 }{ 33 } = 38.86 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 641.26 }{ 42.45 } = 30.21 ; ;

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{ 33**2+42.45**2-42**2 }{ 2 * 33 * 42.45 } ) = 66° 16'50" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 42**2+42.45**2-33**2 }{ 2 * 42 * 42.45 } ) = 46° 1" ; ;
 gamma = 180° - alpha - beta = 180° - 66° 16'50" - 46° 1" = 67° 43'9" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 641.26 }{ 58.73 } = 10.92 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 42 }{ 2 * sin 66° 16'50" } = 22.94 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 33**2+2 * 42.45**2 - 42**2 } }{ 2 } = 31.694 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 42.45**2+2 * 42**2 - 33**2 } }{ 2 } = 38.868 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 33**2+2 * 42**2 - 42.45**2 } }{ 2 } = 31.241 ; ;
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