Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 36   b = 20.78   c = 41.57

Area: T = 374.0439994503
Perimeter: p = 98.35
Semiperimeter: s = 49.175

Angle ∠ A = α = 59.99881350402° = 59°59'53″ = 1.04771650015 rad
Angle ∠ B = β = 29.99220422353° = 29°59'31″ = 0.52334598864 rad
Angle ∠ C = γ = 90.01098227245° = 90°35″ = 1.57109677657 rad

Height: ha = 20.78799996946
Height: hb = 365.999999471
Height: hc = 17.99656696898

Median: ma = 27.4944302137
Median: mb = 37.47110601665
Median: mc = 20.78219146134

Inradius: r = 7.60663039045
Circumradius: R = 20.78550003054

Vertex coordinates: A[41.57; 0] B[0; 0] C[31.1799414241; 17.99656696898]
Centroid: CG[24.2549804747; 5.99985565633]
Coordinates of the circumscribed circle: U[20.785; -0.00435633572]
Coordinates of the inscribed circle: I[28.395; 7.60663039045]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 120.002186496° = 120°7″ = 1.04771650015 rad
∠ B' = β' = 150.0087957765° = 150°29″ = 0.52334598864 rad
∠ C' = γ' = 89.99901772755° = 89°59'25″ = 1.57109677657 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 = 36+20.78+41.57 = 98.35 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 98.35 }{ 2 } = 49.18 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 49.18 * (49.18-36)(49.18-20.78)(49.18-41.57) } ; ; T = sqrt{ 139905.92 } = 374.04 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 374.04 }{ 36 } = 20.78 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 374.04 }{ 20.78 } = 36 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 374.04 }{ 41.57 } = 18 ; ;

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{ 20.78**2+41.57**2-36**2 }{ 2 * 20.78 * 41.57 } ) = 59° 59'53" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 36**2+41.57**2-20.78**2 }{ 2 * 36 * 41.57 } ) = 29° 59'31" ; ;
 gamma = 180° - alpha - beta = 180° - 59° 59'53" - 29° 59'31" = 90° 35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 374.04 }{ 49.18 } = 7.61 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 36 }{ 2 * sin 59° 59'53" } = 20.79 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 20.78**2+2 * 41.57**2 - 36**2 } }{ 2 } = 27.494 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 41.57**2+2 * 36**2 - 20.78**2 } }{ 2 } = 37.471 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 20.78**2+2 * 36**2 - 41.57**2 } }{ 2 } = 20.782 ; ;
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