Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 36   b = 45   c = 14.45

Area: T = 225.2543568367
Perimeter: p = 95.45
Semiperimeter: s = 47.725

Angle ∠ A = α = 43.85438667958° = 43°51'14″ = 0.76553943653 rad
Angle ∠ B = β = 1209.999841024° = 119°59'59″ = 2.09443923277 rad
Angle ∠ C = γ = 16.14662921801° = 16°8'47″ = 0.28218059605 rad

Height: ha = 12.51440871315
Height: hb = 10.01112697052
Height: hc = 31.17769644799

Median: ma = 28.15985022684
Median: mb = 15.68992080743
Median: mc = 40.10436080048

Inradius: r = 4.72198233288
Circumradius: R = 25.98107204939

Vertex coordinates: A[14.45; 0] B[0; 0] C[-187.9999134948; 31.17769644799]
Centroid: CG[-1.18333044983; 10.39223214933]
Coordinates of the circumscribed circle: U[7.225; 24.95659053609]
Coordinates of the inscribed circle: I[2.725; 4.72198233288]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 136.1466133204° = 136°8'46″ = 0.76553943653 rad
∠ B' = β' = 600.0001589759° = 60°1″ = 2.09443923277 rad
∠ C' = γ' = 163.854370782° = 163°51'13″ = 0.28218059605 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 = 36+45+14.45 = 95.45 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 95.45 }{ 2 } = 47.73 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 47.73 * (47.73-36)(47.73-45)(47.73-14.45) } ; ; T = sqrt{ 50739.17 } = 225.25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 225.25 }{ 36 } = 12.51 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 225.25 }{ 45 } = 10.01 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 225.25 }{ 14.45 } = 31.18 ; ;

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{ 45**2+14.45**2-36**2 }{ 2 * 45 * 14.45 } ) = 43° 51'14" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 36**2+14.45**2-45**2 }{ 2 * 36 * 14.45 } ) = 119° 59'59" ; ; gamma = 180° - alpha - beta = 180° - 43° 51'14" - 119° 59'59" = 16° 8'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 225.25 }{ 47.73 } = 4.72 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 36 }{ 2 * sin 43° 51'14" } = 25.98 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 45**2+2 * 14.45**2 - 36**2 } }{ 2 } = 28.159 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 14.45**2+2 * 36**2 - 45**2 } }{ 2 } = 15.689 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 45**2+2 * 36**2 - 14.45**2 } }{ 2 } = 40.104 ; ;
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.