10 10 19 triangle

Obtuse isosceles triangle.

Sides: a = 10   b = 10   c = 19

Area: T = 29.66437404924
Perimeter: p = 39
Semiperimeter: s = 19.5

Angle ∠ A = α = 18.19548723388° = 18°11'42″ = 0.31875604293 rad
Angle ∠ B = β = 18.19548723388° = 18°11'42″ = 0.31875604293 rad
Angle ∠ C = γ = 143.6110255322° = 143°36'37″ = 2.5066471795 rad

Height: ha = 5.93327480985
Height: hb = 5.93327480985
Height: hc = 3.12224989992

Median: ma = 14.33552711868
Median: mb = 14.33552711868
Median: mc = 3.12224989992

Inradius: r = 1.52112174611
Circumradius: R = 16.01328153805

Vertex coordinates: A[19; 0] B[0; 0] C[9.5; 3.12224989992]
Centroid: CG[9.5; 1.04108329997]
Coordinates of the circumscribed circle: U[9.5; -12.89903163813]
Coordinates of the inscribed circle: I[9.5; 1.52112174611]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.8055127661° = 161°48'18″ = 0.31875604293 rad
∠ B' = β' = 161.8055127661° = 161°48'18″ = 0.31875604293 rad
∠ C' = γ' = 36.39897446775° = 36°23'23″ = 2.5066471795 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 = 10 ; ; c = 19 ; ;

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

p = a+b+c = 10+10+19 = 39 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 39 }{ 2 } = 19.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19.5 * (19.5-10)(19.5-10)(19.5-19) } ; ; T = sqrt{ 879.94 } = 29.66 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 29.66 }{ 10 } = 5.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 29.66 }{ 10 } = 5.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 29.66 }{ 19 } = 3.12 ; ;

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**2-10**2-19**2 }{ 2 * 10 * 19 } ) = 18° 11'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 10**2-10**2-19**2 }{ 2 * 10 * 19 } ) = 18° 11'42" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-10**2-10**2 }{ 2 * 10 * 10 } ) = 143° 36'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 29.66 }{ 19.5 } = 1.52 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 18° 11'42" } = 16.01 ; ;




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