Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 0.55   b = 60   c = 59.46

Area: T = 3.11879644922
Perimeter: p = 120.01
Semiperimeter: s = 60.005

Angle ∠ A = α = 0.11001492864° = 0°6'1″ = 0.00217479348 rad
Angle ∠ B = β = 169.0077313272° = 169°26″ = 2.95497340765 rad
Angle ∠ C = γ = 10.89325374415° = 10°53'33″ = 0.19901106423 rad

Height: ha = 11.33880526988
Height: hb = 0.10439321497
Height: hc = 0.1054876034

Median: ma = 59.7329977189
Median: mb = 29.46600924982
Median: mc = 30.2770090023

Inradius: r = 0.05219617447
Circumradius: R = 157.3298603727

Vertex coordinates: A[59.46; 0] B[0; 0] C[-0.54399083417; 0.1054876034]
Centroid: CG[19.64400305528; 0.0354958678]
Coordinates of the circumscribed circle: U[29.73; 154.494406671]
Coordinates of the inscribed circle: I[0.005; 0.05219617447]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 179.9899850714° = 179°53'59″ = 0.00217479348 rad
∠ B' = β' = 10.99326867279° = 10°59'34″ = 2.95497340765 rad
∠ C' = γ' = 169.1077462558° = 169°6'27″ = 0.19901106423 rad

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How did we calculate this triangle?

a = 0.55 ; ; b = 60 ; ; c = 59.46 ; ;

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

p = a+b+c = 0.55+60+59.46 = 120.01 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 120.01 }{ 2 } = 60.01 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 60.01 * (60.01-0.55)(60.01-60)(60.01-59.46) } ; ; T = sqrt{ 9.72 } = 3.12 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3.12 }{ 0.55 } = 11.34 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3.12 }{ 60 } = 0.1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3.12 }{ 59.46 } = 0.1 ; ;

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{ 60**2+59.46**2-0.55**2 }{ 2 * 60 * 59.46 } ) = 0° 6'1" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 0.55**2+59.46**2-60**2 }{ 2 * 0.55 * 59.46 } ) = 169° 26" ; ; gamma = 180° - alpha - beta = 180° - 0° 6'1" - 169° 26" = 10° 53'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3.12 }{ 60.01 } = 0.05 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 0.55 }{ 2 * sin 0° 6'1" } = 157.33 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 60**2+2 * 59.46**2 - 0.55**2 } }{ 2 } = 59.73 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 59.46**2+2 * 0.55**2 - 60**2 } }{ 2 } = 29.46 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 60**2+2 * 0.55**2 - 59.46**2 } }{ 2 } = 30.27 ; ;
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