Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 39   b = 18.19   c = 43.03

Area: T = 354.7054992323
Perimeter: p = 100.22
Semiperimeter: s = 50.11

Angle ∠ A = α = 65.00549630185° = 65°18″ = 1.13545506348 rad
Angle ∠ B = β = 25.0076957954° = 25°25″ = 0.43664537522 rad
Angle ∠ C = γ = 89.98880790275° = 89°59'17″ = 1.57105882666 rad

Height: ha = 18.19899996063
Height: hb = 398.9999991559
Height: hc = 16.4866404477

Median: ma = 26.66441800924
Median: mb = 40.0454617928
Median: mc = 21.51884298916

Inradius: r = 7.07985270869
Circumradius: R = 21.51550004657

Vertex coordinates: A[43.03; 0] B[0; 0] C[35.34440018592; 16.4866404477]
Centroid: CG[26.12546672864; 5.4955468159]
Coordinates of the circumscribed circle: U[21.515; 0.00444764157]
Coordinates of the inscribed circle: I[31.92; 7.07985270869]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 114.9955036981° = 114°59'42″ = 1.13545506348 rad
∠ B' = β' = 154.9933042046° = 154°59'35″ = 0.43664537522 rad
∠ C' = γ' = 90.01219209725° = 90°43″ = 1.57105882666 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 = 39+18.19+43.03 = 100.22 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 100.22 }{ 2 } = 50.11 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 50.11 * (50.11-39)(50.11-18.19)(50.11-43.03) } ; ; T = sqrt{ 125815.63 } = 354.7 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 354.7 }{ 39 } = 18.19 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 354.7 }{ 18.19 } = 39 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 354.7 }{ 43.03 } = 16.49 ; ;

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{ 18.19**2+43.03**2-39**2 }{ 2 * 18.19 * 43.03 } ) = 65° 18" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 39**2+43.03**2-18.19**2 }{ 2 * 39 * 43.03 } ) = 25° 25" ; ;
 gamma = 180° - alpha - beta = 180° - 65° 18" - 25° 25" = 89° 59'17" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 354.7 }{ 50.11 } = 7.08 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 39 }{ 2 * sin 65° 18" } = 21.52 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 18.19**2+2 * 43.03**2 - 39**2 } }{ 2 } = 26.664 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 43.03**2+2 * 39**2 - 18.19**2 } }{ 2 } = 40.045 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 18.19**2+2 * 39**2 - 43.03**2 } }{ 2 } = 21.518 ; ;
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