13 20 25 triangle

Obtuse scalene triangle.

Sides: a = 13   b = 20   c = 25

Area: T = 129.2443955371
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 31.13296133228° = 31°7'47″ = 0.54333142474 rad
Angle ∠ B = β = 52.68880824408° = 52°41'17″ = 0.92195805152 rad
Angle ∠ C = γ = 96.18223042364° = 96°10'56″ = 1.67986978911 rad

Height: ha = 19.88436854417
Height: hb = 12.92443955371
Height: hc = 10.34395164297

Median: ma = 21.68552484422
Median: mb = 17.23436879396
Median: mc = 11.32547516529

Inradius: r = 4.45766881162
Circumradius: R = 12.57331218557

Vertex coordinates: A[25; 0] B[0; 0] C[7.88; 10.34395164297]
Centroid: CG[10.96; 3.44765054766]
Coordinates of the circumscribed circle: U[12.5; -1.35440285075]
Coordinates of the inscribed circle: I[9; 4.45766881162]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.8770386677° = 148°52'13″ = 0.54333142474 rad
∠ B' = β' = 127.3121917559° = 127°18'43″ = 0.92195805152 rad
∠ C' = γ' = 83.81876957636° = 83°49'4″ = 1.67986978911 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 = 13 ; ; b = 20 ; ; c = 25 ; ;

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

p = a+b+c = 13+20+25 = 58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 58 }{ 2 } = 29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29 * (29-13)(29-20)(29-25) } ; ; T = sqrt{ 16704 } = 129.24 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 129.24 }{ 13 } = 19.88 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 129.24 }{ 20 } = 12.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 129.24 }{ 25 } = 10.34 ; ;

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{ 13**2-20**2-25**2 }{ 2 * 20 * 25 } ) = 31° 7'47" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-13**2-25**2 }{ 2 * 13 * 25 } ) = 52° 41'17" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-13**2-20**2 }{ 2 * 20 * 13 } ) = 96° 10'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 129.24 }{ 29 } = 4.46 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 31° 7'47" } = 12.57 ; ;




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