Triangle calculator SSS - result

Please enter the triangle sides:


Right scalene triangle.

Sides: a = 1351.68   b = 1175   c = 1791

Area: T = 7941121.999988
Perimeter: p = 4317.68
Semiperimeter: s = 2158.84

Angle ∠ A = α = 498.9997631036° = 48°59'59″ = 0.85552071989 rad
Angle ∠ B = β = 410.9999270522° = 41° = 0.71655837201 rad
Angle ∠ C = γ = 900.0003098442° = 90°1″ = 1.57108017346 rad

Height: ha = 11754.99999998
Height: hb = 1351.687999998
Height: hc = 886.7810569501

Median: ma = 1355.505481165
Median: mb = 1473.843976782
Median: mc = 895.4955204454

Inradius: r = 367.8421989211
Circumradius: R = 895.5500000013

Vertex coordinates: A[1791; 0] B[0; 0] C[1020.127697443; 886.7810569501]
Centroid: CG[937.0422324809; 295.5943523167]
Coordinates of the circumscribed circle: U[895.5; -0.00548426862]
Coordinates of the inscribed circle: I[983.84; 367.8421989211]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 1311.000236896° = 131°1″ = 0.85552071989 rad
∠ B' = β' = 1399.000072948° = 139° = 0.71655837201 rad
∠ C' = γ' = 909.9996901558° = 89°59'59″ = 1.57108017346 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 = 1351.68+1175+1791 = 4317.68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 4317.68 }{ 2 } = 2158.84 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 2158.84 * (2158.84-1351.68)(2158.84-1175)(2158.84-1791) } ; ; T = sqrt{ 630613868526 } = 794112 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 794112 }{ 1351.68 } = 1175 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 794112 }{ 1175 } = 1351.68 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 794112 }{ 1791 } = 886.78 ; ;

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{ 1175**2+1791**2-1351.68**2 }{ 2 * 1175 * 1791 } ) = 48° 59'59" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 1351.68**2+1791**2-1175**2 }{ 2 * 1351.68 * 1791 } ) = 41° ; ;
 gamma = 180° - alpha - beta = 180° - 48° 59'59" - 41° = 90° 1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 794112 }{ 2158.84 } = 367.84 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 1351.68 }{ 2 * sin 48° 59'59" } = 895.5 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 1175**2+2 * 1791**2 - 1351.68**2 } }{ 2 } = 1355.505 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 1791**2+2 * 1351.68**2 - 1175**2 } }{ 2 } = 1473.84 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 1175**2+2 * 1351.68**2 - 1791**2 } }{ 2 } = 895.495 ; ;
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