1114 1115 1576 triangle

Acute scalene triangle.

Sides: a = 1114   b = 1115   c = 1576

Area: T = 621054.9990036
Perimeter: p = 3805
Semiperimeter: s = 1902.5

Angle ∠ A = α = 44.97994224112° = 44°58'46″ = 0.78550390167 rad
Angle ∠ B = β = 45.03108410204° = 45°1'51″ = 0.78659364407 rad
Angle ∠ C = γ = 89.99897365684° = 89°59'23″ = 1.57106171961 rad

Height: ha = 11154.99998211
Height: hb = 11143.99998213
Height: hc = 788.1410850299

Median: ma = 1246.295510951
Median: mb = 1245.624424109
Median: mc = 788.1411167558

Inradius: r = 326.4421519073
Circumradius: R = 7888.000012643

Vertex coordinates: A[1576; 0] B[0; 0] C[787.2932829949; 788.1410850299]
Centroid: CG[787.764427665; 262.7143616766]
Coordinates of the circumscribed circle: U[788; 0.14111549724]
Coordinates of the inscribed circle: I[787.5; 326.4421519073]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.0210577589° = 135°1'14″ = 0.78550390167 rad
∠ B' = β' = 134.969915898° = 134°58'9″ = 0.78659364407 rad
∠ C' = γ' = 90.01102634316° = 90°37″ = 1.57106171961 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 = 1114 ; ; b = 1115 ; ; c = 1576 ; ;

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

p = a+b+c = 1114+1115+1576 = 3805 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 3805 }{ 2 } = 1902.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1902.5 * (1902.5-1114)(1902.5-1115)(1902.5-1576) } ; ; T = sqrt{ 385709300648 } = 621054.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 621054.99 }{ 1114 } = 1115 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 621054.99 }{ 1115 } = 1114 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 621054.99 }{ 1576 } = 788.14 ; ;

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{ 1115**2+1576**2-1114**2 }{ 2 * 1115 * 1576 } ) = 44° 58'46" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 1114**2+1576**2-1115**2 }{ 2 * 1114 * 1576 } ) = 45° 1'51" ; ;
 gamma = 180° - alpha - beta = 180° - 44° 58'46" - 45° 1'51" = 89° 59'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 621054.99 }{ 1902.5 } = 326.44 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 1114 }{ 2 * sin 44° 58'46" } = 788 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 1115**2+2 * 1576**2 - 1114**2 } }{ 2 } = 1246.295 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 1576**2+2 * 1114**2 - 1115**2 } }{ 2 } = 1245.624 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 1115**2+2 * 1114**2 - 1576**2 } }{ 2 } = 788.141 ; ;
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