11 19 25 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 19   c = 25

Area: T = 98.19546408925
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 24.42218139126° = 24°25'19″ = 0.42662410621 rad
Angle ∠ B = β = 45.57329959992° = 45°34'23″ = 0.79553988302 rad
Angle ∠ C = γ = 110.0055190088° = 110°19″ = 1.92199527613 rad

Height: ha = 17.85435710714
Height: hb = 10.33662779887
Height: hc = 7.85655712714

Median: ma = 21.51216247643
Median: mb = 16.81551717208
Median: mc = 9.20659763198

Inradius: r = 3.57107142143
Circumradius: R = 13.30326607983

Vertex coordinates: A[25; 0] B[0; 0] C[7.7; 7.85655712714]
Centroid: CG[10.9; 2.61985237571]
Coordinates of the circumscribed circle: U[12.5; -4.55109102731]
Coordinates of the inscribed circle: I[8.5; 3.57107142143]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.5788186087° = 155°34'41″ = 0.42662410621 rad
∠ B' = β' = 134.4277004001° = 134°25'37″ = 0.79553988302 rad
∠ C' = γ' = 69.99548099118° = 69°59'41″ = 1.92199527613 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 = 19 ; ; c = 25 ; ;

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

p = a+b+c = 11+19+25 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-11)(27.5-19)(27.5-25) } ; ; T = sqrt{ 9642.19 } = 98.19 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 98.19 }{ 11 } = 17.85 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 98.19 }{ 19 } = 10.34 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 98.19 }{ 25 } = 7.86 ; ;

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**2-19**2-25**2 }{ 2 * 19 * 25 } ) = 24° 25'19" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-11**2-25**2 }{ 2 * 11 * 25 } ) = 45° 34'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-11**2-19**2 }{ 2 * 19 * 11 } ) = 110° 19" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 98.19 }{ 27.5 } = 3.57 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 24° 25'19" } = 13.3 ; ;




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