Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 220   b = 510   c = 614.69

Area: T = 53354.23994886
Perimeter: p = 1344.69
Semiperimeter: s = 672.345

Angle ∠ A = α = 19.99004367677° = 19°54'2″ = 0.34773281442 rad
Angle ∠ B = β = 52.09994605263° = 52°5'58″ = 0.90993071247 rad
Angle ∠ C = γ = 1088.000102706° = 108° = 1.88549573847 rad

Height: ha = 485.0398540805
Height: hb = 209.232231172
Height: hc = 173.5977226207

Median: ma = 553.9660195366
Median: mb = 384.8343597871
Median: mc = 244.5187997242

Inradius: r = 79.35554491943
Circumradius: R = 323.162184553

Vertex coordinates: A[614.69; 0] B[0; 0] C[135.1444378548; 173.5977226207]
Centroid: CG[249.945479285; 57.8665742069]
Coordinates of the circumscribed circle: U[307.345; -99.86330531362]
Coordinates of the inscribed circle: I[162.345; 79.35554491943]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.1099563232° = 160°5'58″ = 0.34773281442 rad
∠ B' = β' = 127.9010539474° = 127°54'2″ = 0.90993071247 rad
∠ C' = γ' = 721.999897294° = 72° = 1.88549573847 rad

Calculate another triangle




How did we calculate this triangle?

a = 220 ; ; b = 510 ; ; c = 614.69 ; ;

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

p = a+b+c = 220+510+614.69 = 1344.69 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1344.69 }{ 2 } = 672.35 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 672.35 * (672.35-220)(672.35-510)(672.35-614.69) } ; ; T = sqrt{ 2846674871.4 } = 53354.24 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 53354.24 }{ 220 } = 485.04 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 53354.24 }{ 510 } = 209.23 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 53354.24 }{ 614.69 } = 173.6 ; ;

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{ 510**2+614.69**2-220**2 }{ 2 * 510 * 614.69 } ) = 19° 54'2" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 220**2+614.69**2-510**2 }{ 2 * 220 * 614.69 } ) = 52° 5'58" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 220**2+510**2-614.69**2 }{ 2 * 220 * 510 } ) = 108° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 53354.24 }{ 672.35 } = 79.36 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 220 }{ 2 * sin 19° 54'2" } = 323.16 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 510**2+2 * 614.69**2 - 220**2 } }{ 2 } = 553.96 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 614.69**2+2 * 220**2 - 510**2 } }{ 2 } = 384.834 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 510**2+2 * 220**2 - 614.69**2 } }{ 2 } = 244.518 ; ;
Calculate another triangle

Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.