363.15 445.21 265.83 triangle

Acute scalene triangle.

Sides: a = 363.15   b = 445.21   c = 265.83

Area: T = 48255.93334112
Perimeter: p = 1074.19
Semiperimeter: s = 537.095

Angle ∠ A = α = 54.63545720825° = 54°38'4″ = 0.95435531683 rad
Angle ∠ B = β = 88.71444644171° = 88°42'52″ = 1.54883594982 rad
Angle ∠ C = γ = 36.65109635004° = 36°39'3″ = 0.64396799871 rad

Height: ha = 265.7633091897
Height: hb = 216.7788299729
Height: hc = 363.0598596932

Median: ma = 318.5422439676
Median: mb = 227.4187610741
Median: mc = 383.8999122264

Inradius: r = 89.84661788161
Circumradius: R = 222.6611042689

Vertex coordinates: A[265.83; 0] B[0; 0] C[8.14772506865; 363.0598596932]
Centroid: CG[91.32657502288; 121.0219532311]
Coordinates of the circumscribed circle: U[132.915; 178.6388021446]
Coordinates of the inscribed circle: I[91.885; 89.84661788161]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.3655427917° = 125°21'56″ = 0.95435531683 rad
∠ B' = β' = 91.28655355829° = 91°17'8″ = 1.54883594982 rad
∠ C' = γ' = 143.34990365° = 143°20'57″ = 0.64396799871 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 = 363.15+445.21+265.83 = 1074.19 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1074.19 }{ 2 } = 537.1 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 537.1 * (537.1-363.15)(537.1-445.21)(537.1-265.83) } ; ; T = sqrt{ 2328635109.39 } = 48255.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 48255.93 }{ 363.15 } = 265.76 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 48255.93 }{ 445.21 } = 216.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 48255.93 }{ 265.83 } = 363.06 ; ;

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{ 445.21**2+265.83**2-363.15**2 }{ 2 * 445.21 * 265.83 } ) = 54° 38'4" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 363.15**2+265.83**2-445.21**2 }{ 2 * 363.15 * 265.83 } ) = 88° 42'52" ; ;
 gamma = 180° - alpha - beta = 180° - 54° 38'4" - 88° 42'52" = 36° 39'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 48255.93 }{ 537.1 } = 89.85 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 363.15 }{ 2 * sin 54° 38'4" } = 222.66 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 445.21**2+2 * 265.83**2 - 363.15**2 } }{ 2 } = 318.542 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 265.83**2+2 * 363.15**2 - 445.21**2 } }{ 2 } = 227.418 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 445.21**2+2 * 363.15**2 - 265.83**2 } }{ 2 } = 383.899 ; ;
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