1732 1414 1000 triangle

Obtuse scalene triangle.

Sides: a = 1732   b = 1414   c = 1000

Area: T = 706999.9921903
Perimeter: p = 4146
Semiperimeter: s = 2073

Angle ∠ A = α = 90.00986713556° = 90°31″ = 1.57109476705 rad
Angle ∠ B = β = 54.72657509471° = 54°43'33″ = 0.95551445397 rad
Angle ∠ C = γ = 35.26655776973° = 35°15'56″ = 0.61655004434 rad

Height: ha = 816.3977219288
Height: hb = 1000.999988548
Height: hc = 14143.99998381

Median: ma = 865.8766434603
Median: mb = 1224.771059076
Median: mc = 1499.876999437

Inradius: r = 341.052161211
Circumradius: R = 8666.000009918

Vertex coordinates: A[1000; 0] B[0; 0] C[1000.214; 14143.99998381]
Centroid: CG[666.738; 471.3333327935]
Coordinates of the circumscribed circle: U[500; 707.0765679951]
Coordinates of the inscribed circle: I[659; 341.052161211]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 89.99113286444° = 89°59'29″ = 1.57109476705 rad
∠ B' = β' = 125.2744249053° = 125°16'27″ = 0.95551445397 rad
∠ C' = γ' = 144.7344422303° = 144°44'4″ = 0.61655004434 rad

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How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 1732 ; ; b = 1414 ; ; c = 1000 ; ;

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

p = a+b+c = 1732+1414+1000 = 4146 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 4146 }{ 2 } = 2073 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 2073 * (2073-1732)(2073-1414)(2073-1000) } ; ; T = sqrt{ 499848988551 } = 706999.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 706999.99 }{ 1732 } = 816.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 706999.99 }{ 1414 } = 1000 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 706999.99 }{ 1000 } = 1414 ; ;

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{ 1414**2+1000**2-1732**2 }{ 2 * 1414 * 1000 } ) = 90° 31" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 1732**2+1000**2-1414**2 }{ 2 * 1732 * 1000 } ) = 54° 43'33" ; ; gamma = 180° - alpha - beta = 180° - 90° 31" - 54° 43'33" = 35° 15'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 706999.99 }{ 2073 } = 341.05 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 1732 }{ 2 * sin 90° 31" } = 866 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 1414**2+2 * 1000**2 - 1732**2 } }{ 2 } = 865.876 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 1000**2+2 * 1732**2 - 1414**2 } }{ 2 } = 1224.771 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 1414**2+2 * 1732**2 - 1000**2 } }{ 2 } = 1499.87 ; ;
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