6 20 25 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 20   c = 25

Area: T = 36.97988791069
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 8.50661469535° = 8°30'22″ = 0.1488460271 rad
Angle ∠ B = β = 29.54113605001° = 29°32'29″ = 0.51655940062 rad
Angle ∠ C = γ = 141.9522492546° = 141°57'9″ = 2.47875383763 rad

Height: ha = 12.32662930356
Height: hb = 3.69878879107
Height: hc = 2.95883103285

Median: ma = 22.43988056723
Median: mb = 15.18222264507
Median: mc = 7.85881168228

Inradius: r = 1.45501521218
Circumradius: R = 20.28218478579

Vertex coordinates: A[25; 0] B[0; 0] C[5.22; 2.95883103285]
Centroid: CG[10.07333333333; 0.98661034428]
Coordinates of the circumscribed circle: U[12.5; -15.97219551881]
Coordinates of the inscribed circle: I[5.5; 1.45501521218]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 171.4943853047° = 171°29'38″ = 0.1488460271 rad
∠ B' = β' = 150.45986395° = 150°27'31″ = 0.51655940062 rad
∠ C' = γ' = 38.04875074536° = 38°2'51″ = 2.47875383763 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 = 6 ; ; b = 20 ; ; c = 25 ; ;

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

p = a+b+c = 6+20+25 = 51 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 51 }{ 2 } = 25.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25.5 * (25.5-6)(25.5-20)(25.5-25) } ; ; T = sqrt{ 1367.44 } = 36.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 36.98 }{ 6 } = 12.33 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 36.98 }{ 20 } = 3.7 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 36.98 }{ 25 } = 2.96 ; ;

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{ 6**2-20**2-25**2 }{ 2 * 20 * 25 } ) = 8° 30'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-6**2-25**2 }{ 2 * 6 * 25 } ) = 29° 32'29" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-6**2-20**2 }{ 2 * 20 * 6 } ) = 141° 57'9" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 36.98 }{ 25.5 } = 1.45 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 8° 30'22" } = 20.28 ; ;




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