Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 53   b = 93   c = 107.84

Area: T = 2464.12771724
Perimeter: p = 253.84
Semiperimeter: s = 126.92

Angle ∠ A = α = 29.43222788748° = 29°25'56″ = 0.51436901727 rad
Angle ∠ B = β = 59.5711093955° = 59°34'16″ = 1.04397117285 rad
Angle ∠ C = γ = 90.99766271702° = 90°59'48″ = 1.58881907523 rad

Height: ha = 92.98659310339
Height: hb = 52.99219822021
Height: hc = 45.76996879154

Median: ma = 97.14441341513
Median: mb = 71.11224658552
Median: mc = 53.11990511963

Inradius: r = 19.41548059596
Circumradius: R = 53.92881582089

Vertex coordinates: A[107.84; 0] B[0; 0] C[26.84328486647; 45.76996879154]
Centroid: CG[44.89442828882; 15.23332293051]
Coordinates of the circumscribed circle: U[53.92; -0.93880020292]
Coordinates of the inscribed circle: I[33.92; 19.41548059596]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.5687721125° = 150°34'4″ = 0.51436901727 rad
∠ B' = β' = 120.4298906045° = 120°25'44″ = 1.04397117285 rad
∠ C' = γ' = 89.00333728298° = 89°12″ = 1.58881907523 rad

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How did we calculate this triangle?

a = 53 ; ; b = 93 ; ; c = 107.84 ; ;

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

p = a+b+c = 53+93+107.84 = 253.84 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 253.84 }{ 2 } = 126.92 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 126.92 * (126.92-53)(126.92-93)(126.92-107.84) } ; ; T = sqrt{ 6071922.72 } = 2464.13 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2464.13 }{ 53 } = 92.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2464.13 }{ 93 } = 52.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2464.13 }{ 107.84 } = 45.7 ; ;

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{ 93**2+107.84**2-53**2 }{ 2 * 93 * 107.84 } ) = 29° 25'56" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 53**2+107.84**2-93**2 }{ 2 * 53 * 107.84 } ) = 59° 34'16" ; ; gamma = 180° - alpha - beta = 180° - 29° 25'56" - 59° 34'16" = 90° 59'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2464.13 }{ 126.92 } = 19.41 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 53 }{ 2 * sin 29° 25'56" } = 53.93 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 93**2+2 * 107.84**2 - 53**2 } }{ 2 } = 97.144 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 107.84**2+2 * 53**2 - 93**2 } }{ 2 } = 71.112 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 93**2+2 * 53**2 - 107.84**2 } }{ 2 } = 53.119 ; ;
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