8 20 25 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 20   c = 25

Area: T = 69.13770920708
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 16.05443080743° = 16°3'16″ = 0.2880200535 rad
Angle ∠ B = β = 43.73987273265° = 43°44'19″ = 0.76333848025 rad
Angle ∠ C = γ = 120.2076964599° = 120°12'25″ = 2.09880073161 rad

Height: ha = 17.28442730177
Height: hb = 6.91437092071
Height: hc = 5.53109673657

Median: ma = 22.28222799552
Median: mb = 15.63664957711
Median: mc = 8.70334475928

Inradius: r = 2.60989468706
Circumradius: R = 14.46440159146

Vertex coordinates: A[25; 0] B[0; 0] C[5.78; 5.53109673657]
Centroid: CG[10.26; 1.84436557886]
Coordinates of the circumscribed circle: U[12.5; -7.2777208007]
Coordinates of the inscribed circle: I[6.5; 2.60989468706]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.9465691926° = 163°56'44″ = 0.2880200535 rad
∠ B' = β' = 136.2611272674° = 136°15'41″ = 0.76333848025 rad
∠ C' = γ' = 59.79330354007° = 59°47'35″ = 2.09880073161 rad

Calculate another triangle




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 = 20 ; ; c = 25 ; ;

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

p = a+b+c = 8+20+25 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-8)(26.5-20)(26.5-25) } ; ; T = sqrt{ 4779.94 } = 69.14 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 69.14 }{ 8 } = 17.28 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 69.14 }{ 20 } = 6.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 69.14 }{ 25 } = 5.53 ; ;

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**2-20**2-25**2 }{ 2 * 20 * 25 } ) = 16° 3'16" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-8**2-25**2 }{ 2 * 8 * 25 } ) = 43° 44'19" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-8**2-20**2 }{ 2 * 20 * 8 } ) = 120° 12'25" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 69.14 }{ 26.5 } = 2.61 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 16° 3'16" } = 14.46 ; ;




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