10 15 19 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 15   c = 19

Area: T = 74.45880418759
Perimeter: p = 44
Semiperimeter: s = 22

Angle ∠ A = α = 31.50109414399° = 31°30'3″ = 0.55497951456 rad
Angle ∠ B = β = 51.60769559808° = 51°36'25″ = 0.90107112988 rad
Angle ∠ C = γ = 96.89221025793° = 96°53'32″ = 1.69110862092 rad

Height: ha = 14.89216083752
Height: hb = 9.92877389168
Height: hc = 7.83876886185

Median: ma = 16.37107055437
Median: mb = 13.22003787824
Median: mc = 8.5

Inradius: r = 3.38444564489
Circumradius: R = 9.56991476978

Vertex coordinates: A[19; 0] B[0; 0] C[6.21105263158; 7.83876886185]
Centroid: CG[8.40435087719; 2.61325628728]
Coordinates of the circumscribed circle: U[9.5; -1.14882977237]
Coordinates of the inscribed circle: I[7; 3.38444564489]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.499905856° = 148°29'57″ = 0.55497951456 rad
∠ B' = β' = 128.3933044019° = 128°23'35″ = 0.90107112988 rad
∠ C' = γ' = 83.10878974207° = 83°6'28″ = 1.69110862092 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 = 10 ; ; b = 15 ; ; c = 19 ; ;

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

p = a+b+c = 10+15+19 = 44 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 44 }{ 2 } = 22 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22 * (22-10)(22-15)(22-19) } ; ; T = sqrt{ 5544 } = 74.46 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 74.46 }{ 10 } = 14.89 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 74.46 }{ 15 } = 9.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 74.46 }{ 19 } = 7.84 ; ;

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{ 10**2-15**2-19**2 }{ 2 * 15 * 19 } ) = 31° 30'3" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-10**2-19**2 }{ 2 * 10 * 19 } ) = 51° 36'25" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-10**2-15**2 }{ 2 * 15 * 10 } ) = 96° 53'32" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 74.46 }{ 22 } = 3.38 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 31° 30'3" } = 9.57 ; ;




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