Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 6   b = 15   c = 19

Area: T = 37.41765738677
Perimeter: p = 40
Semiperimeter: s = 20

Angle ∠ A = α = 15.22327570342° = 15°13'22″ = 0.26656872315 rad
Angle ∠ B = β = 41.02882543699° = 41°1'42″ = 0.71660781251 rad
Angle ∠ C = γ = 123.7498988596° = 123°44'56″ = 2.1659827297 rad

Height: ha = 12.47221912892
Height: hb = 4.98988765157
Height: hc = 3.93985867229

Median: ma = 16.85222995464
Median: mb = 11.92768604419
Median: mc = 6.34442887702

Inradius: r = 1.87108286934
Circumradius: R = 11.42554180918

Vertex coordinates: A[19; 0] B[0; 0] C[4.52663157895; 3.93985867229]
Centroid: CG[7.84221052632; 1.3132862241]
Coordinates of the circumscribed circle: U[9.5; -6.34774544954]
Coordinates of the inscribed circle: I[5; 1.87108286934]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.7777242966° = 164°46'38″ = 0.26656872315 rad
∠ B' = β' = 138.972174563° = 138°58'18″ = 0.71660781251 rad
∠ C' = γ' = 56.25110114041° = 56°15'4″ = 2.1659827297 rad

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How did we calculate this triangle?

a = 6 ; ; b = 15 ; ; c = 19 ; ;

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

p = a+b+c = 6+15+19 = 40 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 40 }{ 2 } = 20 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20 * (20-6)(20-15)(20-19) } ; ; T = sqrt{ 1400 } = 37.42 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 37.42 }{ 6 } = 12.47 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 37.42 }{ 15 } = 4.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 37.42 }{ 19 } = 3.94 ; ;

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**2+19**2-6**2 }{ 2 * 15 * 19 } ) = 15° 13'22" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6**2+19**2-15**2 }{ 2 * 6 * 19 } ) = 41° 1'42" ; ; gamma = 180° - alpha - beta = 180° - 15° 13'22" - 41° 1'42" = 123° 44'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 37.42 }{ 20 } = 1.87 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6 }{ 2 * sin 15° 13'22" } = 11.43 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 15**2+2 * 19**2 - 6**2 } }{ 2 } = 16.852 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 19**2+2 * 6**2 - 15**2 } }{ 2 } = 11.927 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 15**2+2 * 6**2 - 19**2 } }{ 2 } = 6.344 ; ;
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