11 15 19 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 15   c = 19

Area: T = 82.41547286594
Perimeter: p = 45
Semiperimeter: s = 22.5

Angle ∠ A = α = 35.33545017918° = 35°20'4″ = 0.61767033958 rad
Angle ∠ B = β = 52.06602469431° = 52°3'37″ = 0.90986227186 rad
Angle ∠ C = γ = 92.60552512651° = 92°36'19″ = 1.61662665392 rad

Height: ha = 14.98444961199
Height: hb = 10.98986304879
Height: hc = 8.67552345957

Median: ma = 16.21095650774
Median: mb = 13.59222772191
Median: mc = 9.09767026993

Inradius: r = 3.66328768293
Circumradius: R = 9.51098292835

Vertex coordinates: A[19; 0] B[0; 0] C[6.76331578947; 8.67552345957]
Centroid: CG[8.58877192982; 2.89217448652]
Coordinates of the circumscribed circle: U[9.5; -0.43222649674]
Coordinates of the inscribed circle: I[7.5; 3.66328768293]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.6655498208° = 144°39'56″ = 0.61767033958 rad
∠ B' = β' = 127.9439753057° = 127°56'23″ = 0.90986227186 rad
∠ C' = γ' = 87.39547487349° = 87°23'41″ = 1.61662665392 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 = 11 ; ; b = 15 ; ; c = 19 ; ;

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

p = a+b+c = 11+15+19 = 45 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 45 }{ 2 } = 22.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22.5 * (22.5-11)(22.5-15)(22.5-19) } ; ; T = sqrt{ 6792.19 } = 82.41 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 82.41 }{ 11 } = 14.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 82.41 }{ 15 } = 10.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 82.41 }{ 19 } = 8.68 ; ;

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{ 11**2-15**2-19**2 }{ 2 * 15 * 19 } ) = 35° 20'4" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-11**2-19**2 }{ 2 * 11 * 19 } ) = 52° 3'37" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-11**2-15**2 }{ 2 * 15 * 11 } ) = 92° 36'19" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 82.41 }{ 22.5 } = 3.66 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 35° 20'4" } = 9.51 ; ;




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