Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 12.5   b = 3.5   c = 12.98

Area: T = 21.87549994512
Perimeter: p = 28.98
Semiperimeter: s = 14.49

Angle ∠ A = α = 74.37696550624° = 74°22'11″ = 1.29879953444 rad
Angle ∠ B = β = 15.64331791924° = 15°38'35″ = 0.27330249824 rad
Angle ∠ C = γ = 89.98771657453° = 89°59'14″ = 1.57105723268 rad

Height: ha = 3.54999999122
Height: hb = 12.54999996864
Height: hc = 3.37105700233

Median: ma = 7.16325903136
Median: mb = 12.62215173414
Median: mc = 6.49107549638

Inradius: r = 1.51096617979
Circumradius: R = 6.49900001628

Vertex coordinates: A[12.98; 0] B[0; 0] C[12.03769953775; 3.37105700233]
Centroid: CG[8.33989984592; 1.12435233411]
Coordinates of the circumscribed circle: U[6.49; 0.001145376]
Coordinates of the inscribed circle: I[10.99; 1.51096617979]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 105.6330344938° = 105°37'49″ = 1.29879953444 rad
∠ B' = β' = 164.3576820808° = 164°21'25″ = 0.27330249824 rad
∠ C' = γ' = 90.01328342547° = 90°46″ = 1.57105723268 rad

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How did we calculate this triangle?

a = 12.5 ; ; b = 3.5 ; ; c = 12.98 ; ;

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

p = a+b+c = 12.5+3.5+12.98 = 28.98 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 28.98 }{ 2 } = 14.49 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 14.49 * (14.49-12.5)(14.49-3.5)(14.49-12.98) } ; ; T = sqrt{ 478.52 } = 21.87 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 21.87 }{ 12.5 } = 3.5 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 21.87 }{ 3.5 } = 12.5 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 21.87 }{ 12.98 } = 3.37 ; ;

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{ 3.5**2+12.98**2-12.5**2 }{ 2 * 3.5 * 12.98 } ) = 74° 22'11" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 12.5**2+12.98**2-3.5**2 }{ 2 * 12.5 * 12.98 } ) = 15° 38'35" ; ; gamma = 180° - alpha - beta = 180° - 74° 22'11" - 15° 38'35" = 89° 59'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 21.87 }{ 14.49 } = 1.51 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 12.5 }{ 2 * sin 74° 22'11" } = 6.49 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.5**2+2 * 12.98**2 - 12.5**2 } }{ 2 } = 7.163 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.98**2+2 * 12.5**2 - 3.5**2 } }{ 2 } = 12.622 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.5**2+2 * 12.5**2 - 12.98**2 } }{ 2 } = 6.491 ; ;
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