Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 34   b = 46   c = 38.85

Area: T = 646.0144320226
Perimeter: p = 118.85
Semiperimeter: s = 59.425

Angle ∠ A = α = 46.30106521869° = 46°18'2″ = 0.80880988265 rad
Angle ∠ B = β = 77.99986387001° = 77°59'55″ = 1.36113330574 rad
Angle ∠ C = γ = 55.70107091129° = 55°42'3″ = 0.97221607697 rad

Height: ha = 38.00108423662
Height: hb = 28.08875791403
Height: hc = 33.25768504621

Median: ma = 39.03441036787
Median: mb = 28.34989197325
Median: mc = 35.47877306912

Inradius: r = 10.87110865835
Circumradius: R = 23.51439524379

Vertex coordinates: A[38.85; 0] B[0; 0] C[7.07697876448; 33.25768504621]
Centroid: CG[15.30765958816; 11.08656168207]
Coordinates of the circumscribed circle: U[19.425; 13.25504843025]
Coordinates of the inscribed circle: I[13.425; 10.87110865835]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 133.6999347813° = 133°41'58″ = 0.80880988265 rad
∠ B' = β' = 102.00113613° = 102°5″ = 1.36113330574 rad
∠ C' = γ' = 124.2999290887° = 124°17'57″ = 0.97221607697 rad

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How did we calculate this triangle?

a = 34 ; ; b = 46 ; ; c = 38.85 ; ;

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

p = a+b+c = 34+46+38.85 = 118.85 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 118.85 }{ 2 } = 59.43 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 59.43 * (59.43-34)(59.43-46)(59.43-38.85) } ; ; T = sqrt{ 417334.5 } = 646.01 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 646.01 }{ 34 } = 38 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 646.01 }{ 46 } = 28.09 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 646.01 }{ 38.85 } = 33.26 ; ;

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{ 46**2+38.85**2-34**2 }{ 2 * 46 * 38.85 } ) = 46° 18'2" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 34**2+38.85**2-46**2 }{ 2 * 34 * 38.85 } ) = 77° 59'55" ; ; gamma = 180° - alpha - beta = 180° - 46° 18'2" - 77° 59'55" = 55° 42'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 646.01 }{ 59.43 } = 10.87 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 34 }{ 2 * sin 46° 18'2" } = 23.51 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 46**2+2 * 38.85**2 - 34**2 } }{ 2 } = 39.034 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 38.85**2+2 * 34**2 - 46**2 } }{ 2 } = 28.349 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 46**2+2 * 34**2 - 38.85**2 } }{ 2 } = 35.478 ; ;
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