6 22 26 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 22   c = 26

Area: T = 53.24547180479
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 10.72993735799° = 10°43'46″ = 0.18772628956 rad
Angle ∠ B = β = 43.04990798002° = 43°2'57″ = 0.75113481825 rad
Angle ∠ C = γ = 126.222154662° = 126°13'18″ = 2.20329815755 rad

Height: ha = 17.74882393493
Height: hb = 4.84404289134
Height: hc = 4.09657475421

Median: ma = 23.89656062907
Median: mb = 15.33297097168
Median: mc = 9.53993920142

Inradius: r = 1.97220265944
Circumradius: R = 16.11442744568

Vertex coordinates: A[26; 0] B[0; 0] C[4.38546153846; 4.09657475421]
Centroid: CG[10.12882051282; 1.36552491807]
Coordinates of the circumscribed circle: U[13; -9.52220712699]
Coordinates of the inscribed circle: I[5; 1.97220265944]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.271062642° = 169°16'14″ = 0.18772628956 rad
∠ B' = β' = 136.95109202° = 136°57'3″ = 0.75113481825 rad
∠ C' = γ' = 53.77884533802° = 53°46'42″ = 2.20329815755 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 = 6 ; ; b = 22 ; ; c = 26 ; ;

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

p = a+b+c = 6+22+26 = 54 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 54 }{ 2 } = 27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27 * (27-6)(27-22)(27-26) } ; ; T = sqrt{ 2835 } = 53.24 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 53.24 }{ 6 } = 17.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 53.24 }{ 22 } = 4.84 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 53.24 }{ 26 } = 4.1 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 6**2-22**2-26**2 }{ 2 * 22 * 26 } ) = 10° 43'46" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-6**2-26**2 }{ 2 * 6 * 26 } ) = 43° 2'57" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-6**2-22**2 }{ 2 * 22 * 6 } ) = 126° 13'18" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 53.24 }{ 27 } = 1.97 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 10° 43'46" } = 16.11 ; ;




Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.