6 23 26 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 23   c = 26

Area: T = 63.17438672237
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 12.19875989742° = 12°11'51″ = 0.21328882629 rad
Angle ∠ B = β = 54.08882502205° = 54°5'18″ = 0.9444018053 rad
Angle ∠ C = γ = 113.7144150805° = 113°42'51″ = 1.98546863377 rad

Height: ha = 21.05879557412
Height: hb = 5.49333797586
Height: hc = 4.8659528248

Median: ma = 24.36218554302
Median: mb = 14.95882753017
Median: mc = 10.65436378763

Inradius: r = 2.29772315354
Circumradius: R = 14.19989091284

Vertex coordinates: A[26; 0] B[0; 0] C[3.51992307692; 4.8659528248]
Centroid: CG[9.84397435897; 1.62198427493]
Coordinates of the circumscribed circle: U[13; -5.71104308451]
Coordinates of the inscribed circle: I[4.5; 2.29772315354]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.8022401026° = 167°48'9″ = 0.21328882629 rad
∠ B' = β' = 125.912174978° = 125°54'42″ = 0.9444018053 rad
∠ C' = γ' = 66.28658491947° = 66°17'9″ = 1.98546863377 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 = 23 ; ; c = 26 ; ;

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

p = a+b+c = 6+23+26 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-6)(27.5-23)(27.5-26) } ; ; T = sqrt{ 3990.94 } = 63.17 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 63.17 }{ 6 } = 21.06 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 63.17 }{ 23 } = 5.49 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 63.17 }{ 26 } = 4.86 ; ;

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**2-23**2-26**2 }{ 2 * 23 * 26 } ) = 12° 11'51" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-6**2-26**2 }{ 2 * 6 * 26 } ) = 54° 5'18" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-6**2-23**2 }{ 2 * 23 * 6 } ) = 113° 42'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 63.17 }{ 27.5 } = 2.3 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 12° 11'51" } = 14.2 ; ;




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

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