Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 3.61   b = 4.47   c = 4.12

Area: T = 7.00114983111
Perimeter: p = 12.2
Semiperimeter: s = 6.1

Angle ∠ A = α = 49.49554789986° = 49°29'44″ = 0.86438590734 rad
Angle ∠ B = β = 70.30436219861° = 70°18'13″ = 1.22770296797 rad
Angle ∠ C = γ = 60.20108990153° = 60°12'3″ = 1.05107039005 rad

Height: ha = 3.87989464327
Height: hb = 3.13326614367
Height: hc = 3.39987855879

Median: ma = 3.90112337792
Median: mb = 3.16435462696
Median: mc = 3.50218423722

Inradius: r = 1.14877866084
Circumradius: R = 2.37438920245

Vertex coordinates: A[4.12; 0] B[0; 0] C[1.21766990291; 3.39987855879]
Centroid: CG[1.77988996764; 1.13329285293]
Coordinates of the circumscribed circle: U[2.06; 1.18797301996]
Coordinates of the inscribed circle: I[1.63; 1.14877866084]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.5054521001° = 130°30'16″ = 0.86438590734 rad
∠ B' = β' = 109.6966378014° = 109°41'47″ = 1.22770296797 rad
∠ C' = γ' = 119.7999100985° = 119°47'57″ = 1.05107039005 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 = 3.61+4.47+4.12 = 12.2 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 12.2 }{ 2 } = 6.1 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6.1 * (6.1-3.61)(6.1-4.47)(6.1-4.12) } ; ; T = sqrt{ 49.02 } = 7 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 7 }{ 3.61 } = 3.88 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 7 }{ 4.47 } = 3.13 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 7 }{ 4.12 } = 3.4 ; ;

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{ 4.47**2+4.12**2-3.61**2 }{ 2 * 4.47 * 4.12 } ) = 49° 29'44" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 3.61**2+4.12**2-4.47**2 }{ 2 * 3.61 * 4.12 } ) = 70° 18'13" ; ; gamma = 180° - alpha - beta = 180° - 49° 29'44" - 70° 18'13" = 60° 12'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 7 }{ 6.1 } = 1.15 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 3.61 }{ 2 * sin 49° 29'44" } = 2.37 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.47**2+2 * 4.12**2 - 3.61**2 } }{ 2 } = 3.901 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.12**2+2 * 3.61**2 - 4.47**2 } }{ 2 } = 3.164 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.47**2+2 * 3.61**2 - 4.12**2 } }{ 2 } = 3.502 ; ;
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