Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 4.24   b = 3.74   c = 3.74

Area: T = 6.53219398405
Perimeter: p = 11.72
Semiperimeter: s = 5.86

Angle ∠ A = α = 69.06110083197° = 69°3'40″ = 1.20553419799 rad
Angle ∠ B = β = 55.46994958401° = 55°28'10″ = 0.96881253368 rad
Angle ∠ C = γ = 55.46994958401° = 55°28'10″ = 0.96881253368 rad

Height: ha = 3.08111036984
Height: hb = 3.49330159575
Height: hc = 3.49330159575

Median: ma = 3.08111036984
Median: mb = 3.53435110018
Median: mc = 3.53435110018

Inradius: r = 1.11546655018
Circumradius: R = 2.27699008812

Vertex coordinates: A[3.74; 0] B[0; 0] C[2.40334224599; 3.49330159575]
Centroid: CG[2.04878074866; 1.16443386525]
Coordinates of the circumscribed circle: U[1.87; 1.28766817829]
Coordinates of the inscribed circle: I[2.12; 1.11546655018]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 110.939899168° = 110°56'20″ = 1.20553419799 rad
∠ B' = β' = 124.531050416° = 124°31'50″ = 0.96881253368 rad
∠ C' = γ' = 124.531050416° = 124°31'50″ = 0.96881253368 rad

Calculate another triangle




How did we calculate this triangle?

a = 4.24 ; ; b = 3.74 ; ; c = 3.74 ; ;

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

p = a+b+c = 4.24+3.74+3.74 = 11.72 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 11.72 }{ 2 } = 5.86 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 5.86 * (5.86-4.24)(5.86-3.74)(5.86-3.74) } ; ; T = sqrt{ 42.67 } = 6.53 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6.53 }{ 4.24 } = 3.08 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6.53 }{ 3.74 } = 3.49 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6.53 }{ 3.74 } = 3.49 ; ;

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{ 3.74**2+3.74**2-4.24**2 }{ 2 * 3.74 * 3.74 } ) = 69° 3'40" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 4.24**2+3.74**2-3.74**2 }{ 2 * 4.24 * 3.74 } ) = 55° 28'10" ; ; gamma = 180° - alpha - beta = 180° - 69° 3'40" - 55° 28'10" = 55° 28'10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6.53 }{ 5.86 } = 1.11 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 4.24 }{ 2 * sin 69° 3'40" } = 2.27 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.74**2+2 * 3.74**2 - 4.24**2 } }{ 2 } = 3.081 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.74**2+2 * 4.24**2 - 3.74**2 } }{ 2 } = 3.534 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.74**2+2 * 4.24**2 - 3.74**2 } }{ 2 } = 3.534 ; ;
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.