14 15 20 triangle

Acute scalene triangle.

Sides: a = 14   b = 15   c = 20

Area: T = 104.8698667866
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 44.35768008383° = 44°21'24″ = 0.77441722203 rad
Angle ∠ B = β = 48.50991831443° = 48°30'33″ = 0.84766449633 rad
Angle ∠ C = γ = 87.13440160174° = 87°8'2″ = 1.521077547 rad

Height: ha = 14.98112382666
Height: hb = 13.98224890488
Height: hc = 10.48768667866

Median: ma = 16.23326830807
Median: mb = 15.54883118055
Median: mc = 10.51218980208

Inradius: r = 4.28803537905
Circumradius: R = 10.01325234864

Vertex coordinates: A[20; 0] B[0; 0] C[9.275; 10.48768667866]
Centroid: CG[9.75883333333; 3.49656222622]
Coordinates of the circumscribed circle: U[10; 0.50106261743]
Coordinates of the inscribed circle: I[9.5; 4.28803537905]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.6433199162° = 135°38'36″ = 0.77441722203 rad
∠ B' = β' = 131.4910816856° = 131°29'27″ = 0.84766449633 rad
∠ C' = γ' = 92.86659839826° = 92°51'58″ = 1.521077547 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 = 14 ; ; b = 15 ; ; c = 20 ; ;

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

p = a+b+c = 14+15+20 = 49 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 49 }{ 2 } = 24.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24.5 * (24.5-14)(24.5-15)(24.5-20) } ; ; T = sqrt{ 10997.44 } = 104.87 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 104.87 }{ 14 } = 14.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 104.87 }{ 15 } = 13.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 104.87 }{ 20 } = 10.49 ; ;

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{ 14**2-15**2-20**2 }{ 2 * 15 * 20 } ) = 44° 21'24" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-14**2-20**2 }{ 2 * 14 * 20 } ) = 48° 30'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-14**2-15**2 }{ 2 * 15 * 14 } ) = 87° 8'2" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 104.87 }{ 24.5 } = 4.28 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 44° 21'24" } = 10.01 ; ;




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