Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 5   b = 10   c = 12

Area: T = 24.54546022579
Perimeter: p = 27
Semiperimeter: s = 13.5

Angle ∠ A = α = 24.14768479965° = 24°8'49″ = 0.42114420015 rad
Angle ∠ B = β = 54.99003678046° = 54°54'1″ = 0.95881921787 rad
Angle ∠ C = γ = 100.9532784199° = 100°57'10″ = 1.76219584733 rad

Height: ha = 9.81878409032
Height: hb = 4.90989204516
Height: hc = 4.0910767043

Median: ma = 10.75987173957
Median: mb = 7.71436243103
Median: mc = 5.14878150705

Inradius: r = 1.81881186858
Circumradius: R = 6.11113233135

Vertex coordinates: A[12; 0] B[0; 0] C[2.875; 4.0910767043]
Centroid: CG[4.95883333333; 1.36435890143]
Coordinates of the circumscribed circle: U[6; -1.16111514296]
Coordinates of the inscribed circle: I[3.5; 1.81881186858]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.8533152003° = 155°51'11″ = 0.42114420015 rad
∠ B' = β' = 125.1099632195° = 125°5'59″ = 0.95881921787 rad
∠ C' = γ' = 79.04772158011° = 79°2'50″ = 1.76219584733 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 = 5+10+12 = 27 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 27 }{ 2 } = 13.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13.5 * (13.5-5)(13.5-10)(13.5-12) } ; ; T = sqrt{ 602.44 } = 24.54 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 24.54 }{ 5 } = 9.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 24.54 }{ 10 } = 4.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 24.54 }{ 12 } = 4.09 ; ;

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{ 10**2+12**2-5**2 }{ 2 * 10 * 12 } ) = 24° 8'49" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5**2+12**2-10**2 }{ 2 * 5 * 12 } ) = 54° 54'1" ; ;
 gamma = 180° - alpha - beta = 180° - 24° 8'49" - 54° 54'1" = 100° 57'10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 24.54 }{ 13.5 } = 1.82 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5 }{ 2 * sin 24° 8'49" } = 6.11 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 10**2+2 * 12**2 - 5**2 } }{ 2 } = 10.759 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 12**2+2 * 5**2 - 10**2 } }{ 2 } = 7.714 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 10**2+2 * 5**2 - 12**2 } }{ 2 } = 5.148 ; ;
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