Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 38   b = 42   c = 5.75

Area: T = 82.43998904329
Perimeter: p = 85.75
Semiperimeter: s = 42.875

Angle ∠ A = α = 43.03215320784° = 43°1'54″ = 0.75110419169 rad
Angle ∠ B = β = 131.0421655707° = 131°2'30″ = 2.28771083494 rad
Angle ∠ C = γ = 5.92768122145° = 5°55'37″ = 0.10334423873 rad

Height: ha = 4.33768363386
Height: hb = 3.92438043063
Height: hc = 28.66108314549

Median: ma = 23.18547201838
Median: mb = 17.24990941791
Median: mc = 39.94766441019

Inradius: r = 1.92218633337
Circumradius: R = 27.84328768284

Vertex coordinates: A[5.75; 0] B[0; 0] C[-24.95110869565; 28.66108314549]
Centroid: CG[-6.44003623188; 9.5543610485]
Coordinates of the circumscribed circle: U[2.875; 27.69440456612]
Coordinates of the inscribed circle: I[0.875; 1.92218633337]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 136.9688467922° = 136°58'6″ = 0.75110419169 rad
∠ B' = β' = 48.9588344293° = 48°57'30″ = 2.28771083494 rad
∠ C' = γ' = 174.0733187785° = 174°4'23″ = 0.10334423873 rad

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How did we calculate this triangle?

a = 38 ; ; b = 42 ; ; c = 5.75 ; ;

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

p = a+b+c = 38+42+5.75 = 85.75 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 85.75 }{ 2 } = 42.88 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 42.88 * (42.88-38)(42.88-42)(42.88-5.75) } ; ; T = sqrt{ 6789.74 } = 82.4 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 82.4 }{ 38 } = 4.34 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 82.4 }{ 42 } = 3.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 82.4 }{ 5.75 } = 28.66 ; ;

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{ 42**2+5.75**2-38**2 }{ 2 * 42 * 5.75 } ) = 43° 1'54" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 38**2+5.75**2-42**2 }{ 2 * 38 * 5.75 } ) = 131° 2'30" ; ; gamma = 180° - alpha - beta = 180° - 43° 1'54" - 131° 2'30" = 5° 55'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 82.4 }{ 42.88 } = 1.92 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 38 }{ 2 * sin 43° 1'54" } = 27.84 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 42**2+2 * 5.75**2 - 38**2 } }{ 2 } = 23.185 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.75**2+2 * 38**2 - 42**2 } }{ 2 } = 17.249 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 42**2+2 * 38**2 - 5.75**2 } }{ 2 } = 39.947 ; ;
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