Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 270   b = 260   c = 48.42

Area: T = 6251.084403114
Perimeter: p = 578.42
Semiperimeter: s = 289.21

Angle ∠ A = α = 96.74110633073° = 96°44'28″ = 1.68884500766 rad
Angle ∠ B = β = 733.0002018503° = 73°1″ = 1.27440938769 rad
Angle ∠ C = γ = 10.25987348424° = 10°15'31″ = 0.17990487001 rad

Height: ha = 46.30443261566
Height: hb = 48.0855261778
Height: hc = 258.2032562212

Median: ma = 129.4111159488
Median: mb = 143.9522242775
Median: mc = 263.9399151889

Inradius: r = 21.6144342627
Circumradius: R = 135.9439781927

Vertex coordinates: A[48.42; 0] B[0; 0] C[78.93994506402; 258.2032562212]
Centroid: CG[42.45331502134; 86.06875207372]
Coordinates of the circumscribed circle: U[24.21; 133.7676588543]
Coordinates of the inscribed circle: I[29.21; 21.6144342627]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 83.25989366927° = 83°15'32″ = 1.68884500766 rad
∠ B' = β' = 1076.99979815° = 106°59'59″ = 1.27440938769 rad
∠ C' = γ' = 169.7411265158° = 169°44'29″ = 0.17990487001 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 = 270+260+48.42 = 578.42 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 578.42 }{ 2 } = 289.21 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 289.21 * (289.21-270)(289.21-260)(289.21-48.42) } ; ; T = sqrt{ 39076051.56 } = 6251.08 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6251.08 }{ 270 } = 46.3 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6251.08 }{ 260 } = 48.09 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6251.08 }{ 48.42 } = 258.2 ; ;

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{ 260**2+48.42**2-270**2 }{ 2 * 260 * 48.42 } ) = 96° 44'28" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 270**2+48.42**2-260**2 }{ 2 * 270 * 48.42 } ) = 73° 1" ; ;
 gamma = 180° - alpha - beta = 180° - 96° 44'28" - 73° 1" = 10° 15'31" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6251.08 }{ 289.21 } = 21.61 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 270 }{ 2 * sin 96° 44'28" } = 135.94 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 260**2+2 * 48.42**2 - 270**2 } }{ 2 } = 129.411 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 48.42**2+2 * 270**2 - 260**2 } }{ 2 } = 143.952 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 260**2+2 * 270**2 - 48.42**2 } }{ 2 } = 263.939 ; ;
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