4 20 23 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 20   c = 23

Area: T = 28.31985010197
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 7.07224272592° = 7°4'21″ = 0.12334371418 rad
Angle ∠ B = β = 37.99769544166° = 37°59'49″ = 0.66331719603 rad
Angle ∠ C = γ = 134.9310618324° = 134°55'50″ = 2.35549835515 rad

Height: ha = 14.15992505098
Height: hb = 2.8321850102
Height: hc = 2.46224783495

Median: ma = 21.45992637339
Median: mb = 13.13439255366
Median: mc = 8.70334475928

Inradius: r = 1.20550425966
Circumradius: R = 16.24437976389

Vertex coordinates: A[23; 0] B[0; 0] C[3.1522173913; 2.46224783495]
Centroid: CG[8.71773913043; 0.82108261165]
Coordinates of the circumscribed circle: U[11.5; -11.47221820825]
Coordinates of the inscribed circle: I[3.5; 1.20550425966]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 172.9287572741° = 172°55'39″ = 0.12334371418 rad
∠ B' = β' = 142.0033045583° = 142°11″ = 0.66331719603 rad
∠ C' = γ' = 45.06993816758° = 45°4'10″ = 2.35549835515 rad

Calculate another triangle


How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 4 ; ; b = 20 ; ; c = 23 ; ;

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

p = a+b+c = 4+20+23 = 47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 47 }{ 2 } = 23.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23.5 * (23.5-4)(23.5-20)(23.5-23) } ; ; T = sqrt{ 801.94 } = 28.32 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 28.32 }{ 4 } = 14.16 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 28.32 }{ 20 } = 2.83 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 28.32 }{ 23 } = 2.46 ; ;

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{ 20**2+23**2-4**2 }{ 2 * 20 * 23 } ) = 7° 4'21" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 4**2+23**2-20**2 }{ 2 * 4 * 23 } ) = 37° 59'49" ; ; gamma = 180° - alpha - beta = 180° - 7° 4'21" - 37° 59'49" = 134° 55'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 28.32 }{ 23.5 } = 1.21 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 4 }{ 2 * sin 7° 4'21" } = 16.24 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 20**2+2 * 23**2 - 4**2 } }{ 2 } = 21.459 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 23**2+2 * 4**2 - 20**2 } }{ 2 } = 13.134 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 20**2+2 * 4**2 - 23**2 } }{ 2 } = 8.703 ; ;
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.