8 19 25 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 19   c = 25

Area: T = 57.2366352085
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 13.94552833377° = 13°56'43″ = 0.24333911094 rad
Angle ∠ B = β = 34.91552062474° = 34°54'55″ = 0.6099385308 rad
Angle ∠ C = γ = 131.1439510415° = 131°8'22″ = 2.28988162362 rad

Height: ha = 14.30990880213
Height: hb = 6.02548791668
Height: hc = 4.57989081668

Median: ma = 21.84403296678
Median: mb = 15.94552187191
Median: mc = 7.5

Inradius: r = 2.20113981571
Circumradius: R = 16.59878432481

Vertex coordinates: A[25; 0] B[0; 0] C[6.56; 4.57989081668]
Centroid: CG[10.52; 1.52663027223]
Coordinates of the circumscribed circle: U[12.5; -10.92196337159]
Coordinates of the inscribed circle: I[7; 2.20113981571]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.0554716662° = 166°3'17″ = 0.24333911094 rad
∠ B' = β' = 145.0854793753° = 145°5'5″ = 0.6099385308 rad
∠ C' = γ' = 48.86604895851° = 48°51'38″ = 2.28988162362 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 = 8 ; ; b = 19 ; ; c = 25 ; ;

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

p = a+b+c = 8+19+25 = 52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 52 }{ 2 } = 26 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26 * (26-8)(26-19)(26-25) } ; ; T = sqrt{ 3276 } = 57.24 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 57.24 }{ 8 } = 14.31 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 57.24 }{ 19 } = 6.02 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 57.24 }{ 25 } = 4.58 ; ;

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{ 8**2-19**2-25**2 }{ 2 * 19 * 25 } ) = 13° 56'43" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-8**2-25**2 }{ 2 * 8 * 25 } ) = 34° 54'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-8**2-19**2 }{ 2 * 19 * 8 } ) = 131° 8'22" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 57.24 }{ 26 } = 2.2 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 13° 56'43" } = 16.6 ; ;




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