Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 18.76   b = 16.15   c = 27.2

Area: T = 148.1188128052
Perimeter: p = 62.11
Semiperimeter: s = 31.055

Angle ∠ A = α = 42.40550699785° = 42°24'18″ = 0.74401080907 rad
Angle ∠ B = β = 35.48989390369° = 35°29'20″ = 0.61993988342 rad
Angle ∠ C = γ = 102.1065990985° = 102°6'22″ = 1.78220857287 rad

Height: ha = 15.79108452081
Height: hb = 18.34328022355
Height: hc = 10.89110388273

Median: ma = 20.30663253692
Median: mb = 21.92444880214
Median: mc = 11.01990766401

Inradius: r = 4.776954204
Circumradius: R = 13.90993251252

Vertex coordinates: A[27.2; 0] B[0; 0] C[15.27549099265; 10.89110388273]
Centroid: CG[14.15883033088; 3.63303462758]
Coordinates of the circumscribed circle: U[13.6; -2.91770748084]
Coordinates of the inscribed circle: I[14.905; 4.776954204]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.5954930021° = 137°35'42″ = 0.74401080907 rad
∠ B' = β' = 144.5111060963° = 144°30'40″ = 0.61993988342 rad
∠ C' = γ' = 77.89440090155° = 77°53'38″ = 1.78220857287 rad

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How did we calculate this triangle?

a = 18.76 ; ; b = 16.15 ; ; c = 27.2 ; ;

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

p = a+b+c = 18.76+16.15+27.2 = 62.11 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62.11 }{ 2 } = 31.06 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.06 * (31.06-18.76)(31.06-16.15)(31.06-27.2) } ; ; T = sqrt{ 21938.98 } = 148.12 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 148.12 }{ 18.76 } = 15.79 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 148.12 }{ 16.15 } = 18.34 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 148.12 }{ 27.2 } = 10.89 ; ;

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{ 16.15**2+27.2**2-18.76**2 }{ 2 * 16.15 * 27.2 } ) = 42° 24'18" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 18.76**2+27.2**2-16.15**2 }{ 2 * 18.76 * 27.2 } ) = 35° 29'20" ; ; gamma = 180° - alpha - beta = 180° - 42° 24'18" - 35° 29'20" = 102° 6'22" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 148.12 }{ 31.06 } = 4.77 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 18.76 }{ 2 * sin 42° 24'18" } = 13.91 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 16.15**2+2 * 27.2**2 - 18.76**2 } }{ 2 } = 20.306 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 27.2**2+2 * 18.76**2 - 16.15**2 } }{ 2 } = 21.924 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 16.15**2+2 * 18.76**2 - 27.2**2 } }{ 2 } = 11.019 ; ;
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