Triangle calculator SSS - result

Please enter the triangle sides:


Right scalene triangle.

Sides: a = 1180.04   b = 700   c = 950

Area: T = 3325009.999997
Perimeter: p = 2830.04
Semiperimeter: s = 1415.02

Angle ∠ A = α = 909.9997588235° = 89°59'59″ = 1.57107921175 rad
Angle ∠ B = β = 36.38444366822° = 36°23'4″ = 0.63550282166 rad
Angle ∠ C = γ = 53.61658044943° = 53°36'57″ = 0.93657723195 rad

Height: ha = 563.5440218971
Height: hb = 9509.999999992
Height: hc = 7009.999999994

Median: ma = 590.0222372118
Median: mb = 1012.421145414
Median: mc = 845.9454561304

Inradius: r = 234.9799010895
Circumradius: R = 590.0220000005

Vertex coordinates: A[950; 0] B[0; 0] C[949.9977053474; 7009.999999994]
Centroid: CG[633.3322351158; 233.3333333331]
Coordinates of the circumscribed circle: U[475; 349.9988000574]
Coordinates of the inscribed circle: I[715.02; 234.9799010895]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 900.0002411765° = 90°1″ = 1.57107921175 rad
∠ B' = β' = 143.6165563318° = 143°36'56″ = 0.63550282166 rad
∠ C' = γ' = 126.3844195506° = 126°23'3″ = 0.93657723195 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 = 1180.04+700+950 = 2830.04 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 2830.04 }{ 2 } = 1415.02 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1415.02 * (1415.02-1180.04)(1415.02-700)(1415.02-950) } ; ; T = sqrt{ 110556249998 } = 332500 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 332500 }{ 1180.04 } = 563.54 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 332500 }{ 700 } = 950 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 332500 }{ 950 } = 700 ; ;

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{ 700**2+950**2-1180.04**2 }{ 2 * 700 * 950 } ) = 89° 59'59" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 1180.04**2+950**2-700**2 }{ 2 * 1180.04 * 950 } ) = 36° 23'4" ; ; gamma = 180° - alpha - beta = 180° - 89° 59'59" - 36° 23'4" = 53° 36'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 332500 }{ 1415.02 } = 234.98 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 1180.04 }{ 2 * sin 89° 59'59" } = 590.02 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 700**2+2 * 950**2 - 1180.04**2 } }{ 2 } = 590.022 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 950**2+2 * 1180.04**2 - 700**2 } }{ 2 } = 1012.421 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 700**2+2 * 1180.04**2 - 950**2 } }{ 2 } = 845.945 ; ;
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