5 12 13 triangle

Right scalene triangle.

Sides: a = 5   b = 12   c = 13

Area: T = 30
Perimeter: p = 30
Semiperimeter: s = 15

Angle ∠ A = α = 22.6219864948° = 22°37'11″ = 0.39547911197 rad
Angle ∠ B = β = 67.3880135052° = 67°22'49″ = 1.17660052071 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 12
Height: hb = 5
Height: hc = 4.61553846154

Median: ma = 12.25876506721
Median: mb = 7.81102496759
Median: mc = 6.5

Inradius: r = 2
Circumradius: R = 6.5

Vertex coordinates: A[13; 0] B[0; 0] C[1.92330769231; 4.61553846154]
Centroid: CG[4.97443589744; 1.53884615385]
Coordinates of the circumscribed circle: U[6.5; -0]
Coordinates of the inscribed circle: I[3; 2]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.3880135052° = 157°22'49″ = 0.39547911197 rad
∠ B' = β' = 112.6219864948° = 112°37'11″ = 1.17660052071 rad
∠ C' = γ' = 90° = 1.57107963268 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 = 5 ; ; b = 12 ; ; c = 13 ; ;

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

p = a+b+c = 5+12+13 = 30 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 30 }{ 2 } = 15 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 15 * (15-5)(15-12)(15-13) } ; ; T = sqrt{ 900 } = 30 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 30 }{ 5 } = 12 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 30 }{ 12 } = 5 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 30 }{ 13 } = 4.62 ; ;

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{ 5**2-12**2-13**2 }{ 2 * 12 * 13 } ) = 22° 37'11" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-5**2-13**2 }{ 2 * 5 * 13 } ) = 67° 22'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 13**2-5**2-12**2 }{ 2 * 12 * 5 } ) = 90° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 30 }{ 15 } = 2 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 22° 37'11" } = 6.5 ; ;




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