8 19 26 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 19   c = 26

Area: T = 42.87770043263
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 9.99766798764° = 9°59'48″ = 0.17444749781 rad
Angle ∠ B = β = 24.3488071582° = 24°20'53″ = 0.42549540156 rad
Angle ∠ C = γ = 145.6555248542° = 145°39'19″ = 2.54221636599 rad

Height: ha = 10.71992510816
Height: hb = 4.51333688765
Height: hc = 3.2988231102

Median: ma = 22.41765117715
Median: mb = 16.72657286837
Median: mc = 6.59554529791

Inradius: r = 1.61880001633
Circumradius: R = 23.04326545773

Vertex coordinates: A[26; 0] B[0; 0] C[7.28884615385; 3.2988231102]
Centroid: CG[11.09661538462; 1.09994103673]
Coordinates of the circumscribed circle: U[13; -19.02553496674]
Coordinates of the inscribed circle: I[7.5; 1.61880001633]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.0033320124° = 170°12″ = 0.17444749781 rad
∠ B' = β' = 155.6521928418° = 155°39'7″ = 0.42549540156 rad
∠ C' = γ' = 34.34547514583° = 34°20'41″ = 2.54221636599 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 = 8 ; ; b = 19 ; ; c = 26 ; ;

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

p = a+b+c = 8+19+26 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-8)(26.5-19)(26.5-26) } ; ; T = sqrt{ 1838.44 } = 42.88 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 42.88 }{ 8 } = 10.72 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 42.88 }{ 19 } = 4.51 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 42.88 }{ 26 } = 3.3 ; ;

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{ 8**2-19**2-26**2 }{ 2 * 19 * 26 } ) = 9° 59'48" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-8**2-26**2 }{ 2 * 8 * 26 } ) = 24° 20'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-8**2-19**2 }{ 2 * 19 * 8 } ) = 145° 39'19" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 42.88 }{ 26.5 } = 1.62 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 9° 59'48" } = 23.04 ; ;




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

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