8 25 28 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 25   c = 28

Area: T = 97.13987538524
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 16.11333969958° = 16°6'48″ = 0.28112318313 rad
Angle ∠ B = β = 60.14875678299° = 60°8'51″ = 1.05497730957 rad
Angle ∠ C = γ = 103.7399035174° = 103°44'21″ = 1.81105877266 rad

Height: ha = 24.28546884631
Height: hb = 7.77111003082
Height: hc = 6.9388482418

Median: ma = 26.23992835268
Median: mb = 16.3633068172
Median: mc = 12.1866057607

Inradius: r = 3.18548771755
Circumradius: R = 14.4122373481

Vertex coordinates: A[28; 0] B[0; 0] C[3.98221428571; 6.9388482418]
Centroid: CG[10.66107142857; 2.31328274727]
Coordinates of the circumscribed circle: U[14; -3.42329387017]
Coordinates of the inscribed circle: I[5.5; 3.18548771755]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.8876603004° = 163°53'12″ = 0.28112318313 rad
∠ B' = β' = 119.852243217° = 119°51'9″ = 1.05497730957 rad
∠ C' = γ' = 76.26109648256° = 76°15'39″ = 1.81105877266 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 = 25 ; ; c = 28 ; ;

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

p = a+b+c = 8+25+28 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-8)(30.5-25)(30.5-28) } ; ; T = sqrt{ 9435.94 } = 97.14 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 97.14 }{ 8 } = 24.28 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 97.14 }{ 25 } = 7.77 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 97.14 }{ 28 } = 6.94 ; ;

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**2-25**2-28**2 }{ 2 * 25 * 28 } ) = 16° 6'48" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-8**2-28**2 }{ 2 * 8 * 28 } ) = 60° 8'51" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-8**2-25**2 }{ 2 * 25 * 8 } ) = 103° 44'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 97.14 }{ 30.5 } = 3.18 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 16° 6'48" } = 14.41 ; ;




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