Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 336.01   b = 270   c = 200

Area: T = 270009.9999914
Perimeter: p = 806.01
Semiperimeter: s = 403.005

Angle ∠ A = α = 90.00114430579° = 90°5″ = 1.57108215129 rad
Angle ∠ B = β = 53.47702128471° = 53°28'13″ = 0.93332312659 rad
Angle ∠ C = γ = 36.52883440951° = 36°31'42″ = 0.63875398748 rad

Height: ha = 160.7109502642
Height: hb = 2009.999999937
Height: hc = 2709.999999914

Median: ma = 168.0010952304
Median: mb = 241.3011388413
Median: mc = 287.9265962793

Inradius: r = 66.99766873648
Circumradius: R = 168.0055000053

Vertex coordinates: A[200; 0] B[0; 0] C[200.007680025; 2709.999999914]
Centroid: CG[133.3365600083; 909.9999999715]
Coordinates of the circumscribed circle: U[100; 135.0032518654]
Coordinates of the inscribed circle: I[133.005; 66.99766873648]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 89.99985569421° = 89°59'55″ = 1.57108215129 rad
∠ B' = β' = 126.5329787153° = 126°31'47″ = 0.93332312659 rad
∠ C' = γ' = 143.4721655905° = 143°28'18″ = 0.63875398748 rad

Calculate another triangle




How did we calculate this triangle?

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

p = a+b+c = 336.01+270+200 = 806.01 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 806.01 }{ 2 } = 403.01 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 403.01 * (403.01-336.01)(403.01-270)(403.01-200) } ; ; T = sqrt{ 728999999.54 } = 27000 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 27000 }{ 336.01 } = 160.71 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 27000 }{ 270 } = 200 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 27000 }{ 200 } = 270 ; ;

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{ 270**2+200**2-336.01**2 }{ 2 * 270 * 200 } ) = 90° 5" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 336.01**2+200**2-270**2 }{ 2 * 336.01 * 200 } ) = 53° 28'13" ; ; gamma = 180° - alpha - beta = 180° - 90° 5" - 53° 28'13" = 36° 31'42" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 27000 }{ 403.01 } = 67 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 336.01 }{ 2 * sin 90° 5" } = 168.01 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 270**2+2 * 200**2 - 336.01**2 } }{ 2 } = 168.001 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 200**2+2 * 336.01**2 - 270**2 } }{ 2 } = 241.301 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 270**2+2 * 336.01**2 - 200**2 } }{ 2 } = 287.926 ; ;
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.