Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 16   b = 18   c = 28

Area: T = 134.6666254125
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 32.30325452092° = 32°18'9″ = 0.56437857707 rad
Angle ∠ B = β = 36.95550748363° = 36°57'18″ = 0.64549877312 rad
Angle ∠ C = γ = 110.7422379954° = 110°44'33″ = 1.93328191517 rad

Height: ha = 16.83332817656
Height: hb = 14.9632917125
Height: hc = 9.61990181518

Median: ma = 22.13659436212
Median: mb = 20.95223268398
Median: mc = 9.69553597148

Inradius: r = 4.34440727137
Circumradius: R = 14.97703428903

Vertex coordinates: A[28; 0] B[0; 0] C[12.78657142857; 9.61990181518]
Centroid: CG[13.59552380952; 3.20663393839]
Coordinates of the circumscribed circle: U[14; -5.30219964403]
Coordinates of the inscribed circle: I[13; 4.34440727137]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.6977454791° = 147°41'51″ = 0.56437857707 rad
∠ B' = β' = 143.0454925164° = 143°2'42″ = 0.64549877312 rad
∠ C' = γ' = 69.25876200455° = 69°15'27″ = 1.93328191517 rad

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How did we calculate this triangle?

a = 16 ; ; b = 18 ; ; c = 28 ; ;

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

p = a+b+c = 16+18+28 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-16)(31-18)(31-28) } ; ; T = sqrt{ 18135 } = 134.67 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 134.67 }{ 16 } = 16.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 134.67 }{ 18 } = 14.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 134.67 }{ 28 } = 9.62 ; ;

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{ 18**2+28**2-16**2 }{ 2 * 18 * 28 } ) = 32° 18'9" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 16**2+28**2-18**2 }{ 2 * 16 * 28 } ) = 36° 57'18" ; ; gamma = 180° - alpha - beta = 180° - 32° 18'9" - 36° 57'18" = 110° 44'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 134.67 }{ 31 } = 4.34 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 16 }{ 2 * sin 32° 18'9" } = 14.97 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 18**2+2 * 28**2 - 16**2 } }{ 2 } = 22.136 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 16**2 - 18**2 } }{ 2 } = 20.952 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 18**2+2 * 16**2 - 28**2 } }{ 2 } = 9.695 ; ;
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