14 19 30 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 19   c = 30

Area: T = 101.6665812838
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 20.8999027966° = 20°53'57″ = 0.36547568485 rad
Angle ∠ B = β = 28.95550243719° = 28°57'18″ = 0.50553605103 rad
Angle ∠ C = γ = 130.1465947662° = 130°8'45″ = 2.27114752948 rad

Height: ha = 14.52436875483
Height: hb = 10.70216645093
Height: hc = 6.77877208559

Median: ma = 24.11443111036
Median: mb = 21.39550928953
Median: mc = 7.31443694192

Inradius: r = 3.22774861218
Circumradius: R = 19.62331156208

Vertex coordinates: A[30; 0] B[0; 0] C[12.25; 6.77877208559]
Centroid: CG[14.08333333333; 2.25992402853]
Coordinates of the circumscribed circle: U[15; -12.65217455976]
Coordinates of the inscribed circle: I[12.5; 3.22774861218]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.1010972034° = 159°6'3″ = 0.36547568485 rad
∠ B' = β' = 151.0454975628° = 151°2'42″ = 0.50553605103 rad
∠ C' = γ' = 49.85440523379° = 49°51'15″ = 2.27114752948 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 = 19 ; ; c = 30 ; ;

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

p = a+b+c = 14+19+30 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-14)(31.5-19)(31.5-30) } ; ; T = sqrt{ 10335.94 } = 101.67 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 101.67 }{ 14 } = 14.52 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 101.67 }{ 19 } = 10.7 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 101.67 }{ 30 } = 6.78 ; ;

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**2-19**2-30**2 }{ 2 * 19 * 30 } ) = 20° 53'57" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-14**2-30**2 }{ 2 * 14 * 30 } ) = 28° 57'18" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-14**2-19**2 }{ 2 * 19 * 14 } ) = 130° 8'45" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 101.67 }{ 31.5 } = 3.23 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 20° 53'57" } = 19.62 ; ;




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