3 14 15 triangle

Obtuse scalene triangle.

Sides: a = 3   b = 14   c = 15

Area: T = 20.39660780544
Perimeter: p = 32
Semiperimeter: s = 16

Angle ∠ A = α = 11.20108183696° = 11°12'3″ = 0.19554911595 rad
Angle ∠ B = β = 65.02550346323° = 65°1'30″ = 1.13549009506 rad
Angle ∠ C = γ = 103.7744146998° = 103°46'27″ = 1.81112005436 rad

Height: ha = 13.59773853696
Height: hb = 2.91437254363
Height: hc = 2.71994770739

Median: ma = 14.43108696897
Median: mb = 8.24662112512
Median: mc = 6.80107352544

Inradius: r = 1.27547548784
Circumradius: R = 7.72220728211

Vertex coordinates: A[15; 0] B[0; 0] C[1.26766666667; 2.71994770739]
Centroid: CG[5.42222222222; 0.9066492358]
Coordinates of the circumscribed circle: U[7.5; -1.83985887669]
Coordinates of the inscribed circle: I[2; 1.27547548784]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.799918163° = 168°47'57″ = 0.19554911595 rad
∠ B' = β' = 114.9754965368° = 114°58'30″ = 1.13549009506 rad
∠ C' = γ' = 76.2265853002° = 76°13'33″ = 1.81112005436 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 = 3 ; ; b = 14 ; ; c = 15 ; ;

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

p = a+b+c = 3+14+15 = 32 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 32 }{ 2 } = 16 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16 * (16-3)(16-14)(16-15) } ; ; T = sqrt{ 416 } = 20.4 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 20.4 }{ 3 } = 13.6 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 20.4 }{ 14 } = 2.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 20.4 }{ 15 } = 2.72 ; ;

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{ 3**2-14**2-15**2 }{ 2 * 14 * 15 } ) = 11° 12'3" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-3**2-15**2 }{ 2 * 3 * 15 } ) = 65° 1'30" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 15**2-3**2-14**2 }{ 2 * 14 * 3 } ) = 103° 46'27" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 20.4 }{ 16 } = 1.27 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 11° 12'3" } = 7.72 ; ;




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