Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 10.6   b = 8.1   c = 12.08

Area: T = 42.17659455281
Perimeter: p = 30.78
Semiperimeter: s = 15.39

Angle ∠ A = α = 59.55498788408° = 59°33' = 1.03993414549 rad
Angle ∠ B = β = 41.20547714314° = 41°12'17″ = 0.7199158929 rad
Angle ∠ C = γ = 79.24553497278° = 79°14'43″ = 1.38330922696 rad

Height: ha = 7.95877255713
Height: hb = 10.41438137106
Height: hc = 6.98327724384

Median: ma = 8.81435236994
Median: mb = 10.61879423619
Median: mc = 7.24659229916

Inradius: r = 2.74404772923
Circumradius: R = 6.14879878341

Vertex coordinates: A[12.08; 0] B[0; 0] C[7.97550165563; 6.98327724384]
Centroid: CG[6.68550055188; 2.32875908128]
Coordinates of the circumscribed circle: U[6.04; 1.14772377298]
Coordinates of the inscribed circle: I[7.29; 2.74404772923]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 120.4550121159° = 120°27' = 1.03993414549 rad
∠ B' = β' = 138.7955228569° = 138°47'43″ = 0.7199158929 rad
∠ C' = γ' = 100.7554650272° = 100°45'17″ = 1.38330922696 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 = 10.6+8.1+12.08 = 30.78 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 30.78 }{ 2 } = 15.39 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 15.39 * (15.39-10.6)(15.39-8.1)(15.39-12.08) } ; ; T = sqrt{ 1778.81 } = 42.18 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 42.18 }{ 10.6 } = 7.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 42.18 }{ 8.1 } = 10.41 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 42.18 }{ 12.08 } = 6.98 ; ;

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{ 8.1**2+12.08**2-10.6**2 }{ 2 * 8.1 * 12.08 } ) = 59° 33' ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 10.6**2+12.08**2-8.1**2 }{ 2 * 10.6 * 12.08 } ) = 41° 12'17" ; ; gamma = 180° - alpha - beta = 180° - 59° 33' - 41° 12'17" = 79° 14'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 42.18 }{ 15.39 } = 2.74 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 10.6 }{ 2 * sin 59° 33' } = 6.15 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.1**2+2 * 12.08**2 - 10.6**2 } }{ 2 } = 8.814 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.08**2+2 * 10.6**2 - 8.1**2 } }{ 2 } = 10.618 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.1**2+2 * 10.6**2 - 12.08**2 } }{ 2 } = 7.246 ; ;
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