Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 7.21   b = 5.1   c = 3.16

Area: T = 6.99767389357
Perimeter: p = 15.47
Semiperimeter: s = 7.735

Angle ∠ A = α = 119.7398636512° = 119°44'19″ = 2.0989833449 rad
Angle ∠ B = β = 37.89331470309° = 37°53'35″ = 0.66113601796 rad
Angle ∠ C = γ = 22.36882164575° = 22°22'6″ = 0.3990399025 rad

Height: ha = 1.9410842978
Height: hb = 2.74438191905
Height: hc = 4.42883157821

Median: ma = 2.23664648443
Median: mb = 4.94879642278
Median: mc = 6.04215767809

Inradius: r = 0.90545557771
Circumradius: R = 4.15218041858

Vertex coordinates: A[3.16; 0] B[0; 0] C[5.69898259494; 4.42883157821]
Centroid: CG[2.95499419831; 1.47661052607]
Coordinates of the circumscribed circle: U[1.58; 3.83994111524]
Coordinates of the inscribed circle: I[2.635; 0.90545557771]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 60.26113634884° = 60°15'41″ = 2.0989833449 rad
∠ B' = β' = 142.1076852969° = 142°6'25″ = 0.66113601796 rad
∠ C' = γ' = 157.6321783543° = 157°37'54″ = 0.3990399025 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 = 7.21+5.1+3.16 = 15.47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 15.47 }{ 2 } = 7.74 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 7.74 * (7.74-7.21)(7.74-5.1)(7.74-3.16) } ; ; T = sqrt{ 48.95 } = 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 }{ 7.21 } = 1.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 7 }{ 5.1 } = 2.74 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 7 }{ 3.16 } = 4.43 ; ;

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{ 5.1**2+3.16**2-7.21**2 }{ 2 * 5.1 * 3.16 } ) = 119° 44'19" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 7.21**2+3.16**2-5.1**2 }{ 2 * 7.21 * 3.16 } ) = 37° 53'35" ; ; gamma = 180° - alpha - beta = 180° - 119° 44'19" - 37° 53'35" = 22° 22'6" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 7 }{ 7.74 } = 0.9 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 7.21 }{ 2 * sin 119° 44'19" } = 4.15 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.1**2+2 * 3.16**2 - 7.21**2 } }{ 2 } = 2.236 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.16**2+2 * 7.21**2 - 5.1**2 } }{ 2 } = 4.948 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.1**2+2 * 7.21**2 - 3.16**2 } }{ 2 } = 6.042 ; ;
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