Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 6.08   b = 6.4   c = 4.47

Area: T = 12.98877201756
Perimeter: p = 16.95
Semiperimeter: s = 8.475

Angle ∠ A = α = 65.22774321344° = 65°13'39″ = 1.13884334534 rad
Angle ∠ B = β = 72.89548393325° = 72°53'41″ = 1.27222549541 rad
Angle ∠ C = γ = 41.87877285332° = 41°52'40″ = 0.73109042462 rad

Height: ha = 4.27222763735
Height: hb = 4.05986625549
Height: hc = 5.81110604812

Median: ma = 4.6077477618
Median: mb = 4.27700878211
Median: mc = 5.82882051268

Inradius: r = 1.5322474357
Circumradius: R = 3.34880980043

Vertex coordinates: A[4.47; 0] B[0; 0] C[1.78882885906; 5.81110604812]
Centroid: CG[2.08660961969; 1.93770201604]
Coordinates of the circumscribed circle: U[2.235; 2.49328969586]
Coordinates of the inscribed circle: I[2.075; 1.5322474357]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 114.7732567866° = 114°46'21″ = 1.13884334534 rad
∠ B' = β' = 107.1055160668° = 107°6'19″ = 1.27222549541 rad
∠ C' = γ' = 138.1222271467° = 138°7'20″ = 0.73109042462 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 = 6.08+6.4+4.47 = 16.95 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 16.95 }{ 2 } = 8.48 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.48 * (8.48-6.08)(8.48-6.4)(8.48-4.47) } ; ; T = sqrt{ 168.68 } = 12.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 12.99 }{ 6.08 } = 4.27 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 12.99 }{ 6.4 } = 4.06 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 12.99 }{ 4.47 } = 5.81 ; ;

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{ 6.4**2+4.47**2-6.08**2 }{ 2 * 6.4 * 4.47 } ) = 65° 13'39" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6.08**2+4.47**2-6.4**2 }{ 2 * 6.08 * 4.47 } ) = 72° 53'41" ; ; gamma = 180° - alpha - beta = 180° - 65° 13'39" - 72° 53'41" = 41° 52'40" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 12.99 }{ 8.48 } = 1.53 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6.08 }{ 2 * sin 65° 13'39" } = 3.35 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.4**2+2 * 4.47**2 - 6.08**2 } }{ 2 } = 4.607 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.47**2+2 * 6.08**2 - 6.4**2 } }{ 2 } = 4.27 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.4**2+2 * 6.08**2 - 4.47**2 } }{ 2 } = 5.828 ; ;
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