4 12 14 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 12   c = 14

Area: T = 22.24985954613
Perimeter: p = 30
Semiperimeter: s = 15

Angle ∠ A = α = 15.35988855808° = 15°21'32″ = 0.26880631228 rad
Angle ∠ B = β = 52.61768015821° = 52°37' = 0.91883364295 rad
Angle ∠ C = γ = 112.0244312837° = 112°1'28″ = 1.95551931013 rad

Height: ha = 11.12442977306
Height: hb = 3.70880992435
Height: hc = 3.17883707802

Median: ma = 12.88440987267
Median: mb = 8.36766002653
Median: mc = 5.56877643628

Inradius: r = 1.48332396974
Circumradius: R = 7.55110384596

Vertex coordinates: A[14; 0] B[0; 0] C[2.42985714286; 3.17883707802]
Centroid: CG[5.47661904762; 1.05994569267]
Coordinates of the circumscribed circle: U[7; -2.83216394223]
Coordinates of the inscribed circle: I[3; 1.48332396974]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.6411114419° = 164°38'28″ = 0.26880631228 rad
∠ B' = β' = 127.3833198418° = 127°23' = 0.91883364295 rad
∠ C' = γ' = 67.9765687163° = 67°58'32″ = 1.95551931013 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 = 12 ; ; c = 14 ; ;

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

p = a+b+c = 4+12+14 = 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 * (15-4)(15-12)(15-14) } ; ; T = sqrt{ 495 } = 22.25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 22.25 }{ 4 } = 11.12 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 22.25 }{ 12 } = 3.71 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 22.25 }{ 14 } = 3.18 ; ;

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**2-12**2-14**2 }{ 2 * 12 * 14 } ) = 15° 21'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-4**2-14**2 }{ 2 * 4 * 14 } ) = 52° 37' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14**2-4**2-12**2 }{ 2 * 12 * 4 } ) = 112° 1'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 22.25 }{ 15 } = 1.48 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 15° 21'32" } = 7.55 ; ;




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