4 9 12 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 9   c = 12

Area: T = 13.63658901433
Perimeter: p = 25
Semiperimeter: s = 12.5

Angle ∠ A = α = 14.62664748646° = 14°37'35″ = 0.25552801443 rad
Angle ∠ B = β = 34.62221618397° = 34°37'20″ = 0.60442707183 rad
Angle ∠ C = γ = 130.7511363296° = 130°45'5″ = 2.2822041791 rad

Height: ha = 6.81879450716
Height: hb = 3.03301978096
Height: hc = 2.27326483572

Median: ma = 10.4166333328
Median: mb = 7.73298124169
Median: mc = 3.53655339059

Inradius: r = 1.09108712115
Circumradius: R = 7.92202750143

Vertex coordinates: A[12; 0] B[0; 0] C[3.29216666667; 2.27326483572]
Centroid: CG[5.09772222222; 0.75875494524]
Coordinates of the circumscribed circle: U[6; -5.17701795232]
Coordinates of the inscribed circle: I[3.5; 1.09108712115]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.3743525135° = 165°22'25″ = 0.25552801443 rad
∠ B' = β' = 145.378783816° = 145°22'40″ = 0.60442707183 rad
∠ C' = γ' = 49.24986367043° = 49°14'55″ = 2.2822041791 rad

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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 = 4 ; ; b = 9 ; ; c = 12 ; ;

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

p = a+b+c = 4+9+12 = 25 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 25 }{ 2 } = 12.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12.5 * (12.5-4)(12.5-9)(12.5-12) } ; ; T = sqrt{ 185.94 } = 13.64 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 13.64 }{ 4 } = 6.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 13.64 }{ 9 } = 3.03 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 13.64 }{ 12 } = 2.27 ; ;

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{ 4**2-9**2-12**2 }{ 2 * 9 * 12 } ) = 14° 37'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 9**2-4**2-12**2 }{ 2 * 4 * 12 } ) = 34° 37'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 12**2-4**2-9**2 }{ 2 * 9 * 4 } ) = 130° 45'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 13.64 }{ 12.5 } = 1.09 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 14° 37'35" } = 7.92 ; ;




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