Triangle calculator SSS - result

Please enter the triangle sides:


Right scalene triangle.

Sides: a = 51467.91   b = 2584   c = 51403

Area: T = 66412676
Perimeter: p = 105454.91
Semiperimeter: s = 52727.455

Angle ∠ A = α = 900.0000635758° = 90° = 1.57107974364 rad
Angle ∠ B = β = 2.87878041082° = 2°52'40″ = 0.05502271569 rad
Angle ∠ C = γ = 87.1222132316° = 87°7'20″ = 1.52105680603 rad

Height: ha = 2580.741112588
Height: hb = 51403
Height: hc = 2584

Median: ma = 25733.95221364
Median: mb = 51419.23658985
Median: mc = 25831.07224832

Inradius: r = 1259.54663976
Circumradius: R = 25733.955

Vertex coordinates: A[51403; 0] B[0; 0] C[51403.00328672; 2584]
Centroid: CG[34268.66876224; 861.3333333333]
Coordinates of the circumscribed circle: U[25701.5; 1292.029851859]
Coordinates of the inscribed circle: I[50143.455; 1259.54663976]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 909.9999364242° = 90° = 1.57107974364 rad
∠ B' = β' = 177.1222195892° = 177°7'20″ = 0.05502271569 rad
∠ C' = γ' = 92.8787867684° = 92°52'40″ = 1.52105680603 rad

Calculate another triangle




How did we calculate this triangle?

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

p = a+b+c = 51467.91+2584+51403 = 105454.91 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 105454.91 }{ 2 } = 52727.46 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 52727.46 * (52727.46-51467.91)(52727.46-2584)(52727.46-51403) } ; ; T = sqrt{ 4.411 * 10**{ 15 } } = 66412676 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 66412676 }{ 51467.91 } = 2580.74 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 66412676 }{ 2584 } = 51403 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 66412676 }{ 51403 } = 2584 ; ;

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{ 2584**2+51403**2-51467.91**2 }{ 2 * 2584 * 51403 } ) = 90° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 51467.91**2+51403**2-2584**2 }{ 2 * 51467.91 * 51403 } ) = 2° 52'40" ; ; gamma = 180° - alpha - beta = 180° - 90° - 2° 52'40" = 87° 7'20" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 66412676 }{ 52727.46 } = 1259.55 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 51467.91 }{ 2 * sin 90° } = 25733.96 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 2584**2+2 * 51403**2 - 51467.91**2 } }{ 2 } = 25733.952 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 51403**2+2 * 51467.91**2 - 2584**2 } }{ 2 } = 51419.236 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 2584**2+2 * 51467.91**2 - 51403**2 } }{ 2 } = 25831.072 ; ;
Calculate another triangle

Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.