8 12 13 triangle

Acute scalene triangle.

Sides: a = 8   b = 12   c = 13

Area: T = 46.99993351017
Perimeter: p = 33
Semiperimeter: s = 16.5

Angle ∠ A = α = 37.05331475504° = 37°3'11″ = 0.6476699423 rad
Angle ∠ B = β = 64.66766127554° = 64°40' = 1.12986453087 rad
Angle ∠ C = γ = 78.28802396942° = 78°16'49″ = 1.36662479219 rad

Height: ha = 11.75498337754
Height: hb = 7.83332225169
Height: hc = 7.23106669387

Median: ma = 11.85332695911
Median: mb = 8.97221792225
Median: mc = 7.85881168228

Inradius: r = 2.84884445516
Circumradius: R = 6.63883917842

Vertex coordinates: A[13; 0] B[0; 0] C[3.42330769231; 7.23106669387]
Centroid: CG[5.47443589744; 2.41102223129]
Coordinates of the circumscribed circle: U[6.5; 1.34884233312]
Coordinates of the inscribed circle: I[4.5; 2.84884445516]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.947685245° = 142°56'49″ = 0.6476699423 rad
∠ B' = β' = 115.3333387245° = 115°20' = 1.12986453087 rad
∠ C' = γ' = 101.7219760306° = 101°43'11″ = 1.36662479219 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 = 12 ; ; c = 13 ; ;

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

p = a+b+c = 8+12+13 = 33 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 33 }{ 2 } = 16.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16.5 * (16.5-8)(16.5-12)(16.5-13) } ; ; T = sqrt{ 2208.94 } = 47 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 47 }{ 8 } = 11.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 47 }{ 12 } = 7.83 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 47 }{ 13 } = 7.23 ; ;

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**2-12**2-13**2 }{ 2 * 12 * 13 } ) = 37° 3'11" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-8**2-13**2 }{ 2 * 8 * 13 } ) = 64° 40' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 13**2-8**2-12**2 }{ 2 * 12 * 8 } ) = 78° 16'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 47 }{ 16.5 } = 2.85 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 37° 3'11" } = 6.64 ; ;




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

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