Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 10.5   b = 8.7   c = 12.78

Area: T = 45.32438386127
Perimeter: p = 31.98
Semiperimeter: s = 15.99

Angle ∠ A = α = 54.61550171503° = 54°36'54″ = 0.95332118703 rad
Angle ∠ B = β = 42.49443406306° = 42°29'40″ = 0.74216661575 rad
Angle ∠ C = γ = 82.89106422192° = 82°53'26″ = 1.44767146258 rad

Height: ha = 8.63331121167
Height: hb = 10.41992732443
Height: hc = 7.09329324903

Median: ma = 9.58988841895
Median: mb = 10.85766431276
Median: mc = 7.22106578648

Inradius: r = 2.8354511483
Circumradius: R = 6.44395086324

Vertex coordinates: A[12.78; 0] B[0; 0] C[7.74221126761; 7.09329324903]
Centroid: CG[6.84107042254; 2.36443108301]
Coordinates of the circumscribed circle: U[6.39; 0.7976976428]
Coordinates of the inscribed circle: I[7.29; 2.8354511483]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.385498285° = 125°23'6″ = 0.95332118703 rad
∠ B' = β' = 137.5065659369° = 137°30'20″ = 0.74216661575 rad
∠ C' = γ' = 97.10993577808° = 97°6'34″ = 1.44767146258 rad

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How did we calculate this triangle?

a = 10.5 ; ; b = 8.7 ; ; c = 12.78 ; ;

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

p = a+b+c = 10.5+8.7+12.78 = 31.98 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 31.98 }{ 2 } = 15.99 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 15.99 * (15.99-10.5)(15.99-8.7)(15.99-12.78) } ; ; T = sqrt{ 2054.25 } = 45.32 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 45.32 }{ 10.5 } = 8.63 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 45.32 }{ 8.7 } = 10.42 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 45.32 }{ 12.78 } = 7.09 ; ;

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{ 8.7**2+12.78**2-10.5**2 }{ 2 * 8.7 * 12.78 } ) = 54° 36'54" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 10.5**2+12.78**2-8.7**2 }{ 2 * 10.5 * 12.78 } ) = 42° 29'40" ; ; gamma = 180° - alpha - beta = 180° - 54° 36'54" - 42° 29'40" = 82° 53'26" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 45.32 }{ 15.99 } = 2.83 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 10.5 }{ 2 * sin 54° 36'54" } = 6.44 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.7**2+2 * 12.78**2 - 10.5**2 } }{ 2 } = 9.589 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.78**2+2 * 10.5**2 - 8.7**2 } }{ 2 } = 10.857 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.7**2+2 * 10.5**2 - 12.78**2 } }{ 2 } = 7.221 ; ;
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