Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 1.38   b = 1.28   c = 1.15

Area: T = 0.68769745151
Perimeter: p = 3.81
Semiperimeter: s = 1.905

Angle ∠ A = α = 68.96994618317° = 68°58'10″ = 1.20437441923 rad
Angle ∠ B = β = 59.96987287826° = 59°58'7″ = 1.04766517655 rad
Angle ∠ C = γ = 51.06218093858° = 51°3'43″ = 0.89111966958 rad

Height: ha = 0.99656152393
Height: hb = 1.07333976798
Height: hc = 1.19547382871

Median: ma = 1.00221726398
Median: mb = 1.09772009843
Median: mc = 1.22003228732

Inradius: r = 0.36106165434
Circumradius: R = 0.73992413967

Vertex coordinates: A[1.15; 0] B[0; 0] C[0.69106521739; 1.19547382871]
Centroid: CG[0.61435507246; 0.39882460957]
Coordinates of the circumscribed circle: U[0.575; 0.46545996583]
Coordinates of the inscribed circle: I[0.625; 0.36106165434]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 111.0310538168° = 111°1'50″ = 1.20437441923 rad
∠ B' = β' = 120.0311271217° = 120°1'53″ = 1.04766517655 rad
∠ C' = γ' = 128.9388190614° = 128°56'17″ = 0.89111966958 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 = 1.38+1.28+1.15 = 3.81 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 3.81 }{ 2 } = 1.91 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1.91 * (1.91-1.38)(1.91-1.28)(1.91-1.15) } ; ; T = sqrt{ 0.47 } = 0.69 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.69 }{ 1.38 } = 1 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.69 }{ 1.28 } = 1.07 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.69 }{ 1.15 } = 1.19 ; ;

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{ 1.28**2+1.15**2-1.38**2 }{ 2 * 1.28 * 1.15 } ) = 68° 58'10" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 1.38**2+1.15**2-1.28**2 }{ 2 * 1.38 * 1.15 } ) = 59° 58'7" ; ; gamma = 180° - alpha - beta = 180° - 68° 58'10" - 59° 58'7" = 51° 3'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.69 }{ 1.91 } = 0.36 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 1.38 }{ 2 * sin 68° 58'10" } = 0.74 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.28**2+2 * 1.15**2 - 1.38**2 } }{ 2 } = 1.002 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.15**2+2 * 1.38**2 - 1.28**2 } }{ 2 } = 1.097 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.28**2+2 * 1.38**2 - 1.15**2 } }{ 2 } = 1.2 ; ;
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