Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 120   b = 100   c = 46.55

Area: T = 2259.55443747
Perimeter: p = 266.55
Semiperimeter: s = 133.275

Angle ∠ A = α = 103.8788283305° = 103°52'42″ = 1.8133018065 rad
Angle ∠ B = β = 53.99989498333° = 53°59'56″ = 0.94224594672 rad
Angle ∠ C = γ = 22.12327668616° = 22°7'22″ = 0.38661151214 rad

Height: ha = 37.65992395783
Height: hb = 45.1911087494
Height: hc = 97.08107464962

Median: ma = 49.83442377287
Median: mb = 76.04990055819
Median: mc = 107.9733489223

Inradius: r = 16.95440752181
Circumradius: R = 61.80442219137

Vertex coordinates: A[46.55; 0] B[0; 0] C[70.5366009667; 97.08107464962]
Centroid: CG[39.0298669889; 32.36602488321]
Coordinates of the circumscribed circle: U[23.275; 57.2544137155]
Coordinates of the inscribed circle: I[33.275; 16.95440752181]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 76.12217166949° = 76°7'18″ = 1.8133018065 rad
∠ B' = β' = 126.0011050167° = 126°4″ = 0.94224594672 rad
∠ C' = γ' = 157.8777233138° = 157°52'38″ = 0.38661151214 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 = 120+100+46.55 = 266.55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 266.55 }{ 2 } = 133.28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 133.28 * (133.28-120)(133.28-100)(133.28-46.55) } ; ; T = sqrt{ 5105585.97 } = 2259.55 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2259.55 }{ 120 } = 37.66 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2259.55 }{ 100 } = 45.19 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2259.55 }{ 46.55 } = 97.08 ; ;

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{ 100**2+46.55**2-120**2 }{ 2 * 100 * 46.55 } ) = 103° 52'42" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 120**2+46.55**2-100**2 }{ 2 * 120 * 46.55 } ) = 53° 59'56" ; ; gamma = 180° - alpha - beta = 180° - 103° 52'42" - 53° 59'56" = 22° 7'22" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2259.55 }{ 133.28 } = 16.95 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 120 }{ 2 * sin 103° 52'42" } = 61.8 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 100**2+2 * 46.55**2 - 120**2 } }{ 2 } = 49.834 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 46.55**2+2 * 120**2 - 100**2 } }{ 2 } = 76.049 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 100**2+2 * 120**2 - 46.55**2 } }{ 2 } = 107.973 ; ;
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