Triangle calculator

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side a, b and c (hypotenuse-calculated).

Right scalene triangle.

Sides: a = 31   b = 31.8   c = 44.41099088042

Area: T = 492.9
Perimeter: p = 107.2109908804
Semiperimeter: s = 53.60549544021

Angle ∠ A = α = 44.2770156936° = 44°16'13″ = 0.77326599989 rad
Angle ∠ B = β = 45.7329843064° = 45°43'47″ = 0.79881363279 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 31.8
Height: hb = 31
Height: hc = 22.1987748803

Median: ma = 35.37664045658
Median: mb = 34.84397761187
Median: mc = 22.20549544021

Inradius: r = 9.19550455979
Circumradius: R = 22.20549544021

Vertex coordinates: A[44.41099088042; 0] B[0; 0] C[21.63993148708; 22.1987748803]
Centroid: CG[22.01664078917; 7.3999249601]
Coordinates of the circumscribed circle: U[22.20549544021; 0]
Coordinates of the inscribed circle: I[21.80549544021; 9.19550455979]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.7329843064° = 135°43'47″ = 0.77326599989 rad
∠ B' = β' = 134.2770156936° = 134°16'13″ = 0.79881363279 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: side a, b and c (hypotenuse-calculated).

a = 31 ; ; b = 31.8 ; ; c = 44.41 ; ;

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

p = a+b+c = 31+31.8+44.41 = 107.21 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 107.21 }{ 2 } = 53.6 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 53.6 * (53.6-31)(53.6-31.8)(53.6-44.41) } ; ; T = sqrt{ 242950.41 } = 492.9 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 492.9 }{ 31 } = 31.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 492.9 }{ 31.8 } = 31 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 492.9 }{ 44.41 } = 22.2 ; ;

6. 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{ 31.8**2+44.41**2-31**2 }{ 2 * 31.8 * 44.41 } ) = 44° 16'13" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 31**2+44.41**2-31.8**2 }{ 2 * 31 * 44.41 } ) = 45° 43'47" ; ; gamma = 180° - alpha - beta = 180° - 44° 16'13" - 45° 43'47" = 90° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 492.9 }{ 53.6 } = 9.2 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 31 }{ 2 * sin 44° 16'13" } = 22.2 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 31.8**2+2 * 44.41**2 - 31**2 } }{ 2 } = 35.376 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 44.41**2+2 * 31**2 - 31.8**2 } }{ 2 } = 34.84 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 31.8**2+2 * 31**2 - 44.41**2 } }{ 2 } = 22.205 ; ;
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