12 26 29 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 26   c = 29

Area: T = 155.9121633626
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 24.42985843239° = 24°25'43″ = 0.42663592281 rad
Angle ∠ B = β = 63.64328281632° = 63°38'34″ = 1.11107768967 rad
Angle ∠ C = γ = 91.92985875129° = 91°55'43″ = 1.60444565288 rad

Height: ha = 25.9855272271
Height: hb = 11.99332025866
Height: hc = 10.7532526457

Median: ma = 26.87993601114
Median: mb = 17.98661057486
Median: mc = 14.13332940251

Inradius: r = 4.65440786157
Circumradius: R = 14.50882181964

Vertex coordinates: A[29; 0] B[0; 0] C[5.32875862069; 10.7532526457]
Centroid: CG[11.44325287356; 3.58441754857]
Coordinates of the circumscribed circle: U[14.5; -0.48882573431]
Coordinates of the inscribed circle: I[7.5; 4.65440786157]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.5711415676° = 155°34'17″ = 0.42663592281 rad
∠ B' = β' = 116.3577171837° = 116°21'26″ = 1.11107768967 rad
∠ C' = γ' = 88.07114124871° = 88°4'17″ = 1.60444565288 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 = 12 ; ; b = 26 ; ; c = 29 ; ;

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

p = a+b+c = 12+26+29 = 67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67 }{ 2 } = 33.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.5 * (33.5-12)(33.5-26)(33.5-29) } ; ; T = sqrt{ 24308.44 } = 155.91 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 155.91 }{ 12 } = 25.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 155.91 }{ 26 } = 11.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 155.91 }{ 29 } = 10.75 ; ;

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{ 12**2-26**2-29**2 }{ 2 * 26 * 29 } ) = 24° 25'43" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-12**2-29**2 }{ 2 * 12 * 29 } ) = 63° 38'34" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-12**2-26**2 }{ 2 * 26 * 12 } ) = 91° 55'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 155.91 }{ 33.5 } = 4.65 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 24° 25'43" } = 14.51 ; ;




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

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