Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 18.1   b = 15.8   c = 2.66

Area: T = 11.29899158119
Perimeter: p = 36.56
Semiperimeter: s = 18.28

Angle ∠ A = α = 147.5032903557° = 147°30'10″ = 2.57444113233 rad
Angle ∠ B = β = 27.96985383837° = 27°58'7″ = 0.48881430818 rad
Angle ∠ C = γ = 4.52985580591° = 4°31'43″ = 0.07990382485 rad

Height: ha = 1.24875045096
Height: hb = 1.42991032673
Height: hc = 8.48986585052

Median: ma = 6.81658124974
Median: mb = 10.24436712169
Median: mc = 16.93768267394

Inradius: r = 0.61876102742
Circumradius: R = 16.8454828887

Vertex coordinates: A[2.66; 0] B[0; 0] C[15.98660150376; 8.48986585052]
Centroid: CG[6.21553383459; 2.83295528351]
Coordinates of the circumscribed circle: U[1.33; 16.79222410723]
Coordinates of the inscribed circle: I[2.48; 0.61876102742]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 32.49770964428° = 32°29'50″ = 2.57444113233 rad
∠ B' = β' = 152.0311461616° = 152°1'53″ = 0.48881430818 rad
∠ C' = γ' = 175.4711441941° = 175°28'17″ = 0.07990382485 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 = 18.1+15.8+2.66 = 36.56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 36.56 }{ 2 } = 18.28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18.28 * (18.28-18.1)(18.28-15.8)(18.28-2.66) } ; ; T = sqrt{ 127.46 } = 11.29 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 11.29 }{ 18.1 } = 1.25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 11.29 }{ 15.8 } = 1.43 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 11.29 }{ 2.66 } = 8.49 ; ;

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{ 15.8**2+2.66**2-18.1**2 }{ 2 * 15.8 * 2.66 } ) = 147° 30'10" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 18.1**2+2.66**2-15.8**2 }{ 2 * 18.1 * 2.66 } ) = 27° 58'7" ; ; gamma = 180° - alpha - beta = 180° - 147° 30'10" - 27° 58'7" = 4° 31'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 11.29 }{ 18.28 } = 0.62 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 18.1 }{ 2 * sin 147° 30'10" } = 16.84 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 15.8**2+2 * 2.66**2 - 18.1**2 } }{ 2 } = 6.816 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.66**2+2 * 18.1**2 - 15.8**2 } }{ 2 } = 10.244 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 15.8**2+2 * 18.1**2 - 2.66**2 } }{ 2 } = 16.937 ; ;
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