Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 5.1   b = 5.83   c = 10.77

Area: T = 5.00554789981
Perimeter: p = 21.7
Semiperimeter: s = 10.85

Angle ∠ A = α = 9.17442675144° = 9°10'27″ = 0.16601211746 rad
Angle ∠ B = β = 10.50113868921° = 10°30'5″ = 0.18332837773 rad
Angle ∠ C = γ = 160.3244345593° = 160°19'28″ = 2.79881877017 rad

Height: ha = 1.96329329404
Height: hb = 1.71771454539
Height: hc = 0.93295225623

Median: ma = 8.27657718673
Median: mb = 7.90659613584
Median: mc = 1.00106123125

Inradius: r = 0.46113344699
Circumradius: R = 15.99436946157

Vertex coordinates: A[10.77; 0] B[0; 0] C[5.01545775302; 0.93295225623]
Centroid: CG[5.26215258434; 0.31098408541]
Coordinates of the circumscribed circle: U[5.385; -15.06598818873]
Coordinates of the inscribed circle: I[5.02; 0.46113344699]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.8265732486° = 170°49'33″ = 0.16601211746 rad
∠ B' = β' = 169.4998613108° = 169°29'55″ = 0.18332837773 rad
∠ C' = γ' = 19.67656544065° = 19°40'32″ = 2.79881877017 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 = 5.1+5.83+10.77 = 21.7 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 21.7 }{ 2 } = 10.85 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 10.85 * (10.85-5.1)(10.85-5.83)(10.85-10.77) } ; ; T = sqrt{ 25.05 } = 5.01 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5.01 }{ 5.1 } = 1.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5.01 }{ 5.83 } = 1.72 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5.01 }{ 10.77 } = 0.93 ; ;

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{ 5.83**2+10.77**2-5.1**2 }{ 2 * 5.83 * 10.77 } ) = 9° 10'27" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5.1**2+10.77**2-5.83**2 }{ 2 * 5.1 * 10.77 } ) = 10° 30'5" ; ;
 gamma = 180° - alpha - beta = 180° - 9° 10'27" - 10° 30'5" = 160° 19'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5.01 }{ 10.85 } = 0.46 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5.1 }{ 2 * sin 9° 10'27" } = 15.99 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.83**2+2 * 10.77**2 - 5.1**2 } }{ 2 } = 8.276 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 10.77**2+2 * 5.1**2 - 5.83**2 } }{ 2 } = 7.906 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.83**2+2 * 5.1**2 - 10.77**2 } }{ 2 } = 1.001 ; ;
Calculate another triangle


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

See more information about triangles or more details on solving triangles.