8 25 30 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 25   c = 30

Area: T = 84.9565503059
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 13.09439233206° = 13°5'38″ = 0.22985320739 rad
Angle ∠ B = β = 45.06993816758° = 45°4'10″ = 0.78766091021 rad
Angle ∠ C = γ = 121.8376695004° = 121°50'12″ = 2.12664514776 rad

Height: ha = 21.23988757647
Height: hb = 6.79664402447
Height: hc = 5.66437002039

Median: ma = 27.32221521846
Median: mb = 18.04985456478
Median: mc = 10.93216055545

Inradius: r = 2.69770000971
Circumradius: R = 17.65663017814

Vertex coordinates: A[30; 0] B[0; 0] C[5.65; 5.66437002039]
Centroid: CG[11.88333333333; 1.8887900068]
Coordinates of the circumscribed circle: U[15; -9.31436991897]
Coordinates of the inscribed circle: I[6.5; 2.69770000971]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.9066076679° = 166°54'22″ = 0.22985320739 rad
∠ B' = β' = 134.9310618324° = 134°55'50″ = 0.78766091021 rad
∠ C' = γ' = 58.16333049964° = 58°9'48″ = 2.12664514776 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 = 30 ; ;

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

p = a+b+c = 8+25+30 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-8)(31.5-25)(31.5-30) } ; ; T = sqrt{ 7217.44 } = 84.96 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 84.96 }{ 8 } = 21.24 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 84.96 }{ 25 } = 6.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 84.96 }{ 30 } = 5.66 ; ;

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**2-30**2 }{ 2 * 25 * 30 } ) = 13° 5'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-8**2-30**2 }{ 2 * 8 * 30 } ) = 45° 4'10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-8**2-25**2 }{ 2 * 25 * 8 } ) = 121° 50'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 84.96 }{ 31.5 } = 2.7 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 13° 5'38" } = 17.66 ; ;




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