Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 76.79   b = 133   c = 153.58

Area: T = 5106.535499243
Perimeter: p = 363.37
Semiperimeter: s = 181.685

Angle ∠ A = α = 309.999999951° = 30° = 0.52435987747 rad
Angle ∠ B = β = 59.99768800227° = 59°59'49″ = 1.04771430973 rad
Angle ∠ C = γ = 90.00331200264° = 90°11″ = 1.57108507815 rad

Height: ha = 1332.999999803
Height: hb = 76.79899998861
Height: hc = 66.54999999014

Median: ma = 138.4333132505
Median: mb = 101.5854990279
Median: mc = 76.78663786749

Inradius: r = 28.10765304919
Circumradius: R = 76.79900001139

Vertex coordinates: A[153.58; 0] B[0; 0] C[38.39986212397; 66.54999999014]
Centroid: CG[63.99328737466; 22.16766666338]
Coordinates of the circumscribed circle: U[76.79; -0.0044181579]
Coordinates of the inscribed circle: I[48.685; 28.10765304919]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 1500.000000049° = 150° = 0.52435987747 rad
∠ B' = β' = 120.0033119977° = 120°11″ = 1.04771430973 rad
∠ C' = γ' = 89.99768799736° = 89°59'49″ = 1.57108507815 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 = 76.79+133+153.58 = 363.37 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 363.37 }{ 2 } = 181.69 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 181.69 * (181.69-76.79)(181.69-133)(181.69-153.58) } ; ; T = sqrt{ 26076699.63 } = 5106.53 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5106.53 }{ 76.79 } = 133 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5106.53 }{ 133 } = 76.79 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5106.53 }{ 153.58 } = 66.5 ; ;

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{ 133**2+153.58**2-76.79**2 }{ 2 * 133 * 153.58 } ) = 30° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 76.79**2+153.58**2-133**2 }{ 2 * 76.79 * 153.58 } ) = 59° 59'49" ; ; gamma = 180° - alpha - beta = 180° - 30° - 59° 59'49" = 90° 11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5106.53 }{ 181.69 } = 28.11 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 76.79 }{ 2 * sin 30° } = 76.79 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 133**2+2 * 153.58**2 - 76.79**2 } }{ 2 } = 138.433 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 153.58**2+2 * 76.79**2 - 133**2 } }{ 2 } = 101.585 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 133**2+2 * 76.79**2 - 153.58**2 } }{ 2 } = 76.786 ; ;
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