Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 101   b = 65   c = 105.01

Area: T = 3170.611093748
Perimeter: p = 271.01
Semiperimeter: s = 135.505

Angle ∠ A = α = 68.28438446568° = 68°17'2″ = 1.19217779152 rad
Angle ∠ B = β = 36.71988923336° = 36°43'8″ = 0.64108655689 rad
Angle ∠ C = γ = 74.99772630096° = 74°59'50″ = 1.30989491695 rad

Height: ha = 62.78443749996
Height: hb = 97.55772596147
Height: hc = 60.38768381579

Median: ma = 71.24546492728
Median: mb = 97.76440018105
Median: mc = 66.75549621751

Inradius: r = 23.39884792995
Circumradius: R = 54.35878716842

Vertex coordinates: A[105.01; 0] B[0; 0] C[80.95994329112; 60.38768381579]
Centroid: CG[61.99898109704; 20.12989460526]
Coordinates of the circumscribed circle: U[52.505; 14.07113605965]
Coordinates of the inscribed circle: I[70.505; 23.39884792995]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 111.7166155343° = 111°42'58″ = 1.19217779152 rad
∠ B' = β' = 143.2811107666° = 143°16'52″ = 0.64108655689 rad
∠ C' = γ' = 105.003273699° = 105°10″ = 1.30989491695 rad

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How did we calculate this triangle?

a = 101 ; ; b = 65 ; ; c = 105.01 ; ;

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

p = a+b+c = 101+65+105.01 = 271.01 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 271.01 }{ 2 } = 135.51 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 135.51 * (135.51-101)(135.51-65)(135.51-105.01) } ; ; T = sqrt{ 10052773.72 } = 3170.61 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3170.61 }{ 101 } = 62.78 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3170.61 }{ 65 } = 97.56 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3170.61 }{ 105.01 } = 60.39 ; ;

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{ 65**2+105.01**2-101**2 }{ 2 * 65 * 105.01 } ) = 68° 17'2" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 101**2+105.01**2-65**2 }{ 2 * 101 * 105.01 } ) = 36° 43'8" ; ; gamma = 180° - alpha - beta = 180° - 68° 17'2" - 36° 43'8" = 74° 59'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3170.61 }{ 135.51 } = 23.4 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 101 }{ 2 * sin 68° 17'2" } = 54.36 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 65**2+2 * 105.01**2 - 101**2 } }{ 2 } = 71.245 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 105.01**2+2 * 101**2 - 65**2 } }{ 2 } = 97.764 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 65**2+2 * 101**2 - 105.01**2 } }{ 2 } = 66.755 ; ;
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