Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 11   b = 16   c = 22

Area: T = 83.8365776969
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 28.44766098654° = 28°26'48″ = 0.49664870032 rad
Angle ∠ B = β = 43.85767453647° = 43°51'24″ = 0.76554446058 rad
Angle ∠ C = γ = 107.697664477° = 107°41'48″ = 1.88796610446 rad

Height: ha = 15.24328685398
Height: hb = 10.47994721211
Height: hc = 7.62114342699

Median: ma = 18.43223085912
Median: mb = 15.44334452115
Median: mc = 8.21658383626

Inradius: r = 3.42218684477
Circumradius: R = 11.54663831194

Vertex coordinates: A[22; 0] B[0; 0] C[7.93218181818; 7.62114342699]
Centroid: CG[9.97772727273; 2.544047809]
Coordinates of the circumscribed circle: U[11; -3.51098380505]
Coordinates of the inscribed circle: I[8.5; 3.42218684477]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.5533390135° = 151°33'12″ = 0.49664870032 rad
∠ B' = β' = 136.1433254635° = 136°8'36″ = 0.76554446058 rad
∠ C' = γ' = 72.30333552301° = 72°18'12″ = 1.88796610446 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 = 11+16+22 = 49 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 49 }{ 2 } = 24.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24.5 * (24.5-11)(24.5-16)(24.5-22) } ; ; T = sqrt{ 7028.44 } = 83.84 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 83.84 }{ 11 } = 15.24 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 83.84 }{ 16 } = 10.48 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 83.84 }{ 22 } = 7.62 ; ;

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**2+22**2-11**2 }{ 2 * 16 * 22 } ) = 28° 26'48" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 11**2+22**2-16**2 }{ 2 * 11 * 22 } ) = 43° 51'24" ; ; gamma = 180° - alpha - beta = 180° - 28° 26'48" - 43° 51'24" = 107° 41'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 83.84 }{ 24.5 } = 3.42 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 11 }{ 2 * sin 28° 26'48" } = 11.55 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 22**2 - 11**2 } }{ 2 } = 18.432 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 22**2+2 * 11**2 - 16**2 } }{ 2 } = 15.443 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 11**2 - 22**2 } }{ 2 } = 8.216 ; ;
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