Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 59   b = 4.36   c = 62

Area: T = 95.64326536345
Perimeter: p = 125.36
Semiperimeter: s = 62.68

Angle ∠ A = α = 45.04220410558° = 45°2'31″ = 0.78661319182 rad
Angle ∠ B = β = 2.99774964103° = 2°59'51″ = 0.05223161817 rad
Angle ∠ C = γ = 131.9660462534° = 131°57'38″ = 2.30331445537 rad

Height: ha = 3.2422123852
Height: hb = 43.87327768965
Height: hc = 3.08552468914

Median: ma = 32.57769059304
Median: mb = 60.47993154723
Median: mc = 28.08992292525

Inradius: r = 1.5265887901
Circumradius: R = 41.68987220135

Vertex coordinates: A[62; 0] B[0; 0] C[58.91992774194; 3.08552468914]
Centroid: CG[40.30664258065; 1.02884156305]
Coordinates of the circumscribed circle: U[31; -27.87438146496]
Coordinates of the inscribed circle: I[58.32; 1.5265887901]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.9587958944° = 134°57'29″ = 0.78661319182 rad
∠ B' = β' = 177.003250359° = 177°9″ = 0.05223161817 rad
∠ C' = γ' = 48.04395374662° = 48°2'22″ = 2.30331445537 rad

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How did we calculate this triangle?

a = 59 ; ; b = 4.36 ; ; c = 62 ; ;

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

p = a+b+c = 59+4.36+62 = 125.36 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 125.36 }{ 2 } = 62.68 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 62.68 * (62.68-59)(62.68-4.36)(62.68-62) } ; ; T = sqrt{ 9147.52 } = 95.64 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 95.64 }{ 59 } = 3.24 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 95.64 }{ 4.36 } = 43.87 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 95.64 }{ 62 } = 3.09 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 59**2-4.36**2-62**2 }{ 2 * 4.36 * 62 } ) = 45° 2'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4.36**2-59**2-62**2 }{ 2 * 59 * 62 } ) = 2° 59'51" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 62**2-59**2-4.36**2 }{ 2 * 4.36 * 59 } ) = 131° 57'38" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 95.64 }{ 62.68 } = 1.53 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 59 }{ 2 * sin 45° 2'31" } = 41.69 ; ;

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