Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 2.9   b = 7.49   c = 6.2

Area: T = 8.68774811151
Perimeter: p = 16.59
Semiperimeter: s = 8.295

Angle ∠ A = α = 21.97220328993° = 21°58'19″ = 0.38334843174 rad
Angle ∠ B = β = 104.9065943454° = 104°54'21″ = 1.83109541182 rad
Angle ∠ C = γ = 53.12220236467° = 53°7'19″ = 0.9277154218 rad

Height: ha = 5.99113662862
Height: hb = 2.32197546369
Height: hc = 2.80224132629

Median: ma = 6.72106807691
Median: mb = 3.06659378663
Median: mc = 4.75986815401

Inradius: r = 1.04773153846
Circumradius: R = 3.87554098632

Vertex coordinates: A[6.2; 0] B[0; 0] C[-0.74659758065; 2.80224132629]
Centroid: CG[1.81880080645; 0.93441377543]
Coordinates of the circumscribed circle: U[3.1; 2.32656830412]
Coordinates of the inscribed circle: I[0.805; 1.04773153846]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.0287967101° = 158°1'41″ = 0.38334843174 rad
∠ B' = β' = 75.0944056546° = 75°5'39″ = 1.83109541182 rad
∠ C' = γ' = 126.8787976353° = 126°52'41″ = 0.9277154218 rad

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How did we calculate this triangle?

a = 2.9 ; ; b = 7.49 ; ; c = 6.2 ; ;

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

p = a+b+c = 2.9+7.49+6.2 = 16.59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 16.59 }{ 2 } = 8.3 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.3 * (8.3-2.9)(8.3-7.49)(8.3-6.2) } ; ; T = sqrt{ 75.47 } = 8.69 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 8.69 }{ 2.9 } = 5.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 8.69 }{ 7.49 } = 2.32 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 8.69 }{ 6.2 } = 2.8 ; ;

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{ 7.49**2+6.2**2-2.9**2 }{ 2 * 7.49 * 6.2 } ) = 21° 58'19" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 2.9**2+6.2**2-7.49**2 }{ 2 * 2.9 * 6.2 } ) = 104° 54'21" ; ; gamma = 180° - alpha - beta = 180° - 21° 58'19" - 104° 54'21" = 53° 7'19" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 8.69 }{ 8.3 } = 1.05 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 2.9 }{ 2 * sin 21° 58'19" } = 3.88 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.49**2+2 * 6.2**2 - 2.9**2 } }{ 2 } = 6.721 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.2**2+2 * 2.9**2 - 7.49**2 } }{ 2 } = 3.066 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.49**2+2 * 2.9**2 - 6.2**2 } }{ 2 } = 4.759 ; ;
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