Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 4   b = 8   c = 10

Area: T = 15.19986841536
Perimeter: p = 22
Semiperimeter: s = 11

Angle ∠ A = α = 22.33216450092° = 22°19'54″ = 0.39897607328 rad
Angle ∠ B = β = 49.45883981265° = 49°27'30″ = 0.86332118901 rad
Angle ∠ C = γ = 108.2109956864° = 108°12'36″ = 1.88986200307 rad

Height: ha = 7.59993420768
Height: hb = 3.87996710384
Height: hc = 3.04397368307

Median: ma = 8.83217608663
Median: mb = 6.48107406984
Median: mc = 3.87329833462

Inradius: r = 1.38216985594
Circumradius: R = 5.26436135597

Vertex coordinates: A[10; 0] B[0; 0] C[2.6; 3.04397368307]
Centroid: CG[4.2; 1.01332456102]
Coordinates of the circumscribed circle: U[5; -1.64548792374]
Coordinates of the inscribed circle: I[3; 1.38216985594]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.6688354991° = 157°40'6″ = 0.39897607328 rad
∠ B' = β' = 130.5421601874° = 130°32'30″ = 0.86332118901 rad
∠ C' = γ' = 71.79900431357° = 71°47'24″ = 1.88986200307 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 = 4+8+10 = 22 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 22 }{ 2 } = 11 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11 * (11-4)(11-8)(11-10) } ; ; T = sqrt{ 231 } = 15.2 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 15.2 }{ 4 } = 7.6 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 15.2 }{ 8 } = 3.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 15.2 }{ 10 } = 3.04 ; ;

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{ 8**2+10**2-4**2 }{ 2 * 8 * 10 } ) = 22° 19'54" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 4**2+10**2-8**2 }{ 2 * 4 * 10 } ) = 49° 27'30" ; ; gamma = 180° - alpha - beta = 180° - 22° 19'54" - 49° 27'30" = 108° 12'36" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 15.2 }{ 11 } = 1.38 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 4 }{ 2 * sin 22° 19'54" } = 5.26 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 8**2+2 * 10**2 - 4**2 } }{ 2 } = 8.832 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 10**2+2 * 4**2 - 8**2 } }{ 2 } = 6.481 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 8**2+2 * 4**2 - 10**2 } }{ 2 } = 3.873 ; ;
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.