Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 7.28   b = 15.3   c = 8.06

Area: T = 4.22990295057
Perimeter: p = 30.64
Semiperimeter: s = 15.32

Angle ∠ A = α = 3.93328552556° = 3°55'58″ = 0.06986412732 rad
Angle ∠ B = β = 171.7122138363° = 171°42'44″ = 2.99769421801 rad
Angle ∠ C = γ = 4.35550063818° = 4°21'18″ = 0.07660092003 rad

Height: ha = 1.16218212928
Height: hb = 0.55328143145
Height: hc = 1.04993869741

Median: ma = 11.67437825918
Median: mb = 0.67771262807
Median: mc = 11.28328764063

Inradius: r = 0.27660463124
Circumradius: R = 53.07109846545

Vertex coordinates: A[8.06; 0] B[0; 0] C[-7.20439702233; 1.04993869741]
Centroid: CG[0.28553432589; 0.3549795658]
Coordinates of the circumscribed circle: U[4.03; 52.91877523351]
Coordinates of the inscribed circle: I[0.02; 0.27660463124]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 176.0677144744° = 176°4'2″ = 0.06986412732 rad
∠ B' = β' = 8.28878616375° = 8°17'16″ = 2.99769421801 rad
∠ C' = γ' = 175.6454993618° = 175°38'42″ = 0.07660092003 rad

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How did we calculate this triangle?

a = 7.28 ; ; b = 15.3 ; ; c = 8.06 ; ;

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

p = a+b+c = 7.28+15.3+8.06 = 30.64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 30.64 }{ 2 } = 15.32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 15.32 * (15.32-7.28)(15.32-15.3)(15.32-8.06) } ; ; T = sqrt{ 17.88 } = 4.23 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4.23 }{ 7.28 } = 1.16 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4.23 }{ 15.3 } = 0.55 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4.23 }{ 8.06 } = 1.05 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 7.28**2-15.3**2-8.06**2 }{ 2 * 15.3 * 8.06 } ) = 3° 55'58" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15.3**2-7.28**2-8.06**2 }{ 2 * 7.28 * 8.06 } ) = 171° 42'44" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 8.06**2-7.28**2-15.3**2 }{ 2 * 15.3 * 7.28 } ) = 4° 21'18" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4.23 }{ 15.32 } = 0.28 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7.28 }{ 2 * sin 3° 55'58" } = 53.07 ; ;

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