Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 200   b = 180   c = 302.54

Area: T = 173533.0001397
Perimeter: p = 682.54
Semiperimeter: s = 341.27

Angle ∠ A = α = 39.59113632734° = 39°35'29″ = 0.69109996445 rad
Angle ∠ B = β = 355.0000430814° = 35° = 0.61108659901 rad
Angle ∠ C = γ = 105.4098593645° = 105°24'31″ = 1.8439727019 rad

Height: ha = 173.5330001397
Height: hb = 192.8111112663
Height: hc = 114.7155410456

Median: ma = 227.9598824791
Median: mb = 240.1365848636
Median: mc = 115.4010983965

Inradius: r = 50.84883023404
Circumradius: R = 156.9110043109

Vertex coordinates: A[302.54; 0] B[0; 0] C[163.8330322602; 114.7155410456]
Centroid: CG[155.4576774201; 38.23884701521]
Coordinates of the circumscribed circle: U[151.27; -41.69111109064]
Coordinates of the inscribed circle: I[161.27; 50.84883023404]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.4098636727° = 140°24'31″ = 0.69109996445 rad
∠ B' = β' = 1454.999956919° = 145° = 0.61108659901 rad
∠ C' = γ' = 74.59114063547° = 74°35'29″ = 1.8439727019 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 = 200+180+302.54 = 682.54 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 682.54 }{ 2 } = 341.27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 341.27 * (341.27-200)(341.27-180)(341.27-302.54) } ; ; T = sqrt{ 301126613.85 } = 17353 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 17353 }{ 200 } = 173.53 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 17353 }{ 180 } = 192.81 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 17353 }{ 302.54 } = 114.72 ; ;

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{ 180**2+302.54**2-200**2 }{ 2 * 180 * 302.54 } ) = 39° 35'29" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 200**2+302.54**2-180**2 }{ 2 * 200 * 302.54 } ) = 35° ; ; gamma = 180° - alpha - beta = 180° - 39° 35'29" - 35° = 105° 24'31" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 17353 }{ 341.27 } = 50.85 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 200 }{ 2 * sin 39° 35'29" } = 156.91 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 180**2+2 * 302.54**2 - 200**2 } }{ 2 } = 227.959 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 302.54**2+2 * 200**2 - 180**2 } }{ 2 } = 240.136 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 180**2+2 * 200**2 - 302.54**2 } }{ 2 } = 115.401 ; ;
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