9 22 26 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 22   c = 26

Area: T = 95.03112448619
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 19.40770433824° = 19°24'25″ = 0.33987168051 rad
Angle ∠ B = β = 54.31546652873° = 54°18'53″ = 0.94879697414 rad
Angle ∠ C = γ = 106.278829133° = 106°16'42″ = 1.85549061071 rad

Height: ha = 21.11880544138
Height: hb = 8.63992040784
Height: hc = 7.31100957586

Median: ma = 23.65990363286
Median: mb = 16.04768065359
Median: mc = 10.65436378763

Inradius: r = 3.33444296443
Circumradius: R = 13.54329142475

Vertex coordinates: A[26; 0] B[0; 0] C[5.25; 7.31100957586]
Centroid: CG[10.41766666667; 2.43766985862]
Coordinates of the circumscribed circle: U[13; -3.79661199027]
Coordinates of the inscribed circle: I[6.5; 3.33444296443]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.5932956618° = 160°35'35″ = 0.33987168051 rad
∠ B' = β' = 125.6855334713° = 125°41'7″ = 0.94879697414 rad
∠ C' = γ' = 73.72217086698° = 73°43'18″ = 1.85549061071 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 = 9 ; ; b = 22 ; ; c = 26 ; ;

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

p = a+b+c = 9+22+26 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-9)(28.5-22)(28.5-26) } ; ; T = sqrt{ 9030.94 } = 95.03 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 95.03 }{ 9 } = 21.12 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 95.03 }{ 22 } = 8.64 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 95.03 }{ 26 } = 7.31 ; ;

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{ 9**2-22**2-26**2 }{ 2 * 22 * 26 } ) = 19° 24'25" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-9**2-26**2 }{ 2 * 9 * 26 } ) = 54° 18'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-9**2-22**2 }{ 2 * 22 * 9 } ) = 106° 16'42" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 95.03 }{ 28.5 } = 3.33 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 19° 24'25" } = 13.54 ; ;




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

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