Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 7   b = 4.61   c = 6.36

Area: T = 14.31217578274
Perimeter: p = 17.97
Semiperimeter: s = 8.985

Angle ∠ A = α = 77.49901376067° = 77°29'25″ = 1.35224580391 rad
Angle ∠ B = β = 40.01111079478° = 40°40″ = 0.69883255711 rad
Angle ∠ C = γ = 62.49987544455° = 62°29'56″ = 1.09108090435 rad

Height: ha = 4.0899073665
Height: hb = 6.2099005565
Height: hc = 4.50105527759

Median: ma = 4.3132870274
Median: mb = 6.27878798173
Median: mc = 5.00113648137

Inradius: r = 1.59328500643
Circumradius: R = 3.58551151633

Vertex coordinates: A[6.36; 0] B[0; 0] C[5.36114386792; 4.50105527759]
Centroid: CG[3.90771462264; 1.55001842586]
Coordinates of the circumscribed circle: U[3.18; 1.65554910854]
Coordinates of the inscribed circle: I[4.375; 1.59328500643]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 102.5109862393° = 102°30'35″ = 1.35224580391 rad
∠ B' = β' = 139.9898892052° = 139°59'20″ = 0.69883255711 rad
∠ C' = γ' = 117.5011245555° = 117°30'4″ = 1.09108090435 rad

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How did we calculate this triangle?

a = 7 ; ; b = 4.61 ; ; c = 6.36 ; ;

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

p = a+b+c = 7+4.61+6.36 = 17.97 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 17.97 }{ 2 } = 8.99 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.99 * (8.99-7)(8.99-4.61)(8.99-6.36) } ; ; T = sqrt{ 204.83 } = 14.31 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 14.31 }{ 7 } = 4.09 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 14.31 }{ 4.61 } = 6.21 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 14.31 }{ 6.36 } = 4.5 ; ;

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{ 4.61**2+6.36**2-7**2 }{ 2 * 4.61 * 6.36 } ) = 77° 29'25" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 7**2+6.36**2-4.61**2 }{ 2 * 7 * 6.36 } ) = 40° 40" ; ; gamma = 180° - alpha - beta = 180° - 77° 29'25" - 40° 40" = 62° 29'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 14.31 }{ 8.99 } = 1.59 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 7 }{ 2 * sin 77° 29'25" } = 3.59 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.61**2+2 * 6.36**2 - 7**2 } }{ 2 } = 4.313 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.36**2+2 * 7**2 - 4.61**2 } }{ 2 } = 6.278 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.61**2+2 * 7**2 - 6.36**2 } }{ 2 } = 5.001 ; ;
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