8 23 25 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 23   c = 25

Area: T = 91.65215138991
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 18.59896365026° = 18°35'23″ = 0.32444503637 rad
Angle ∠ B = β = 66.42218215218° = 66°25'19″ = 1.15992794807 rad
Angle ∠ C = γ = 94.98985419756° = 94°59'19″ = 1.65878628091 rad

Height: ha = 22.91328784748
Height: hb = 7.97696968608
Height: hc = 7.33221211119

Median: ma = 23.68554385647
Median: mb = 14.56988022843
Median: mc = 11.84327192823

Inradius: r = 3.27332683535
Circumradius: R = 12.54875286886

Vertex coordinates: A[25; 0] B[0; 0] C[3.2; 7.33221211119]
Centroid: CG[9.4; 2.44440403706]
Coordinates of the circumscribed circle: U[12.5; -1.09110894512]
Coordinates of the inscribed circle: I[5; 3.27332683535]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.4110363497° = 161°24'37″ = 0.32444503637 rad
∠ B' = β' = 113.5788178478° = 113°34'41″ = 1.15992794807 rad
∠ C' = γ' = 85.01114580244° = 85°41″ = 1.65878628091 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 = 23 ; ; c = 25 ; ;

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

p = a+b+c = 8+23+25 = 56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 56 }{ 2 } = 28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28 * (28-8)(28-23)(28-25) } ; ; T = sqrt{ 8400 } = 91.65 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 91.65 }{ 8 } = 22.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 91.65 }{ 23 } = 7.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 91.65 }{ 25 } = 7.33 ; ;

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**2-23**2-25**2 }{ 2 * 23 * 25 } ) = 18° 35'23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-8**2-25**2 }{ 2 * 8 * 25 } ) = 66° 25'19" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-8**2-23**2 }{ 2 * 23 * 8 } ) = 94° 59'19" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 91.65 }{ 28 } = 3.27 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 18° 35'23" } = 12.55 ; ;




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