1015 1035 1450 triangle

Obtuse scalene triangle.

Sides: a = 1015   b = 1035   c = 1450

Area: T = 525262.4344408
Perimeter: p = 3500
Semiperimeter: s = 1750

Angle ∠ A = α = 44.42769969877° = 44°25'37″ = 0.77553973742 rad
Angle ∠ B = β = 45.54443694382° = 45°32'40″ = 0.79548992024 rad
Angle ∠ C = γ = 90.02986335742° = 90°1'43″ = 1.57112960769 rad

Height: ha = 10354.99987075
Height: hb = 10154.99987325
Height: hc = 724.5499909528

Median: ma = 1152.955544146
Median: mb = 1139.542212296
Median: mc = 724.638784058

Inradius: r = 300.1549962519
Circumradius: R = 7255.000090535

Vertex coordinates: A[1450; 0] B[0; 0] C[710.8622068966; 724.5499909528]
Centroid: CG[720.2877356322; 241.5499969843]
Coordinates of the circumscribed circle: U[725; -0.36223188858]
Coordinates of the inscribed circle: I[715; 300.1549962519]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.5733003012° = 135°34'23″ = 0.77553973742 rad
∠ B' = β' = 134.4565630562° = 134°27'20″ = 0.79548992024 rad
∠ C' = γ' = 89.97113664258° = 89°58'17″ = 1.57112960769 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 = 1015 ; ; b = 1035 ; ; c = 1450 ; ;

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

p = a+b+c = 1015+1035+1450 = 3500 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 3500 }{ 2 } = 1750 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1750 * (1750-1015)(1750-1035)(1750-1450) } ; ; T = sqrt{ 275900625000 } = 525262.43 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 525262.43 }{ 1015 } = 1035 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 525262.43 }{ 1035 } = 1015 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 525262.43 }{ 1450 } = 724.5 ; ;

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{ 1035**2+1450**2-1015**2 }{ 2 * 1035 * 1450 } ) = 44° 25'37" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 1015**2+1450**2-1035**2 }{ 2 * 1015 * 1450 } ) = 45° 32'40" ; ; gamma = 180° - alpha - beta = 180° - 44° 25'37" - 45° 32'40" = 90° 1'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 525262.43 }{ 1750 } = 300.15 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 1015 }{ 2 * sin 44° 25'37" } = 725 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 1035**2+2 * 1450**2 - 1015**2 } }{ 2 } = 1152.955 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 1450**2+2 * 1015**2 - 1035**2 } }{ 2 } = 1139.542 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 1035**2+2 * 1015**2 - 1450**2 } }{ 2 } = 724.638 ; ;
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