Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 105   b = 85.77   c = 127.23

Area: T = 4469.393322734
Perimeter: p = 318
Semiperimeter: s = 159

Angle ∠ A = α = 54.99879474164° = 54°59'53″ = 0.96598952643 rad
Angle ∠ B = β = 41.99986744414° = 41°59'55″ = 0.73330151505 rad
Angle ∠ C = γ = 83.00333781423° = 83°12″ = 1.44986822389 rad

Height: ha = 85.13112995684
Height: hb = 104.2188100206
Height: hc = 70.25769083917

Median: ma = 94.95112132624
Median: mb = 108.4766325643
Median: mc = 71.72108353618

Inradius: r = 28.10993913669
Circumradius: R = 64.09222736721

Vertex coordinates: A[127.23; 0] B[0; 0] C[78.03218321151; 70.25769083917]
Centroid: CG[68.4210610705; 23.41989694639]
Coordinates of the circumscribed circle: U[63.615; 7.80771326017]
Coordinates of the inscribed circle: I[73.23; 28.10993913669]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.0022052584° = 125°7″ = 0.96598952643 rad
∠ B' = β' = 138.0011325559° = 138°5″ = 0.73330151505 rad
∠ C' = γ' = 96.99766218577° = 96°59'48″ = 1.44986822389 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 = 105+85.77+127.23 = 318 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 318 }{ 2 } = 159 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 159 * (159-105)(159-85.77)(159-127.23) } ; ; T = sqrt{ 19975475.82 } = 4469.39 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4469.39 }{ 105 } = 85.13 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4469.39 }{ 85.77 } = 104.22 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4469.39 }{ 127.23 } = 70.26 ; ;

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{ 85.77**2+127.23**2-105**2 }{ 2 * 85.77 * 127.23 } ) = 54° 59'53" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 105**2+127.23**2-85.77**2 }{ 2 * 105 * 127.23 } ) = 41° 59'55" ; ; gamma = 180° - alpha - beta = 180° - 54° 59'53" - 41° 59'55" = 83° 12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4469.39 }{ 159 } = 28.11 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 105 }{ 2 * sin 54° 59'53" } = 64.09 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 85.77**2+2 * 127.23**2 - 105**2 } }{ 2 } = 94.951 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 127.23**2+2 * 105**2 - 85.77**2 } }{ 2 } = 108.476 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 85.77**2+2 * 105**2 - 127.23**2 } }{ 2 } = 71.721 ; ;
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.