Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 1.06   b = 0.87   c = 0.92

Area: T = 0.38218088977
Perimeter: p = 2.85
Semiperimeter: s = 1.425

Angle ∠ A = α = 72.5632656645° = 72°33'46″ = 1.26664572724 rad
Angle ∠ B = β = 51.5399498188° = 51°32'22″ = 0.98995339382 rad
Angle ∠ C = γ = 55.8987845167° = 55°53'52″ = 0.97656014429 rad

Height: ha = 0.72203941466
Height: hb = 0.87877216039
Height: hc = 0.83300193429

Median: ma = 0.72216300992
Median: mb = 0.89220622176
Median: mc = 0.85436099812

Inradius: r = 0.26879360686
Circumradius: R = 0.55655292223

Vertex coordinates: A[0.92; 0] B[0; 0] C[0.65992934783; 0.83300193429]
Centroid: CG[0.52664311594; 0.27766731143]
Coordinates of the circumscribed circle: U[0.46; 0.31114686449]
Coordinates of the inscribed circle: I[0.555; 0.26879360686]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 107.4377343355° = 107°26'14″ = 1.26664572724 rad
∠ B' = β' = 128.4610501812° = 128°27'38″ = 0.98995339382 rad
∠ C' = γ' = 124.1022154833° = 124°6'8″ = 0.97656014429 rad

Calculate another triangle




How did we calculate this triangle?

a = 1.06 ; ; b = 0.87 ; ; c = 0.92 ; ;

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

p = a+b+c = 1.06+0.87+0.92 = 2.85 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 2.85 }{ 2 } = 1.43 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1.43 * (1.43-1.06)(1.43-0.87)(1.43-0.92) } ; ; T = sqrt{ 0.15 } = 0.38 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.38 }{ 1.06 } = 0.72 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.38 }{ 0.87 } = 0.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.38 }{ 0.92 } = 0.83 ; ;

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{ 0.87**2+0.92**2-1.06**2 }{ 2 * 0.87 * 0.92 } ) = 72° 33'46" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 1.06**2+0.92**2-0.87**2 }{ 2 * 1.06 * 0.92 } ) = 51° 32'22" ; ; gamma = 180° - alpha - beta = 180° - 72° 33'46" - 51° 32'22" = 55° 53'52" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.38 }{ 1.43 } = 0.27 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 1.06 }{ 2 * sin 72° 33'46" } = 0.56 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.87**2+2 * 0.92**2 - 1.06**2 } }{ 2 } = 0.722 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.92**2+2 * 1.06**2 - 0.87**2 } }{ 2 } = 0.892 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.87**2+2 * 1.06**2 - 0.92**2 } }{ 2 } = 0.854 ; ;
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.