Triangle calculator

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side a, b and c.

Obtuse isosceles triangle.

Sides: a = 50   b = 50   c = 84

Area: T = 1139.431143717
Perimeter: p = 184
Semiperimeter: s = 92

Angle ∠ A = α = 32.86598803789° = 32°51'36″ = 0.57435131044 rad
Angle ∠ B = β = 32.86598803789° = 32°51'36″ = 0.57435131044 rad
Angle ∠ C = γ = 114.2880239242° = 114°16'49″ = 1.99545664447 rad

Height: ha = 45.57772574866
Height: hb = 45.57772574866
Height: hc = 27.12993199325

Median: ma = 64.44437739429
Median: mb = 64.44437739429
Median: mc = 27.12993199325

Inradius: r = 12.3855124317
Circumradius: R = 46.07656112984

Vertex coordinates: A[84; 0] B[0; 0] C[42; 27.12993199325]
Centroid: CG[42; 9.04331066442]
Coordinates of the circumscribed circle: U[42; -18.94662913659]
Coordinates of the inscribed circle: I[42; 12.3855124317]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.1440119621° = 147°8'24″ = 0.57435131044 rad
∠ B' = β' = 147.1440119621° = 147°8'24″ = 0.57435131044 rad
∠ C' = γ' = 65.72197607578° = 65°43'11″ = 1.99545664447 rad

Calculate another triangle


How did we calculate this triangle?

1. Input data entered: side a, b and c.

a = 50 ; ; b = 50 ; ; c = 84 ; ;

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

p = a+b+c = 50+50+84 = 184 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 184 }{ 2 } = 92 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 92 * (92-50)(92-50)(92-84) } ; ; T = sqrt{ 1298304 } = 1139.43 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1139.43 }{ 50 } = 45.58 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1139.43 }{ 50 } = 45.58 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1139.43 }{ 84 } = 27.13 ; ;

6. 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{ 50**2+84**2-50**2 }{ 2 * 50 * 84 } ) = 32° 51'36" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 50**2+84**2-50**2 }{ 2 * 50 * 84 } ) = 32° 51'36" ; ; gamma = 180° - alpha - beta = 180° - 32° 51'36" - 32° 51'36" = 114° 16'49" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1139.43 }{ 92 } = 12.39 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 50 }{ 2 * sin 32° 51'36" } = 46.08 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 50**2+2 * 84**2 - 50**2 } }{ 2 } = 64.444 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 84**2+2 * 50**2 - 50**2 } }{ 2 } = 64.444 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 50**2+2 * 50**2 - 84**2 } }{ 2 } = 27.129 ; ;
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.