17 21 25 triangle

Acute scalene triangle.

Sides: a = 17   b = 21   c = 25

Area: T = 176.5599303068
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 42.26985844296° = 42°16'7″ = 0.73877259685 rad
Angle ∠ B = β = 56.18879349057° = 56°11'17″ = 0.9810664464 rad
Angle ∠ C = γ = 81.54334806647° = 81°32'37″ = 1.42332022211 rad

Height: ha = 20.77216827139
Height: hb = 16.81551717208
Height: hc = 14.12547442455

Median: ma = 21.46550879337
Median: mb = 18.62112244495
Median: mc = 14.44881832768

Inradius: r = 5.60550572403
Circumradius: R = 12.63773969608

Vertex coordinates: A[25; 0] B[0; 0] C[9.46; 14.12547442455]
Centroid: CG[11.48766666667; 4.70882480818]
Coordinates of the circumscribed circle: U[12.5; 1.85884407295]
Coordinates of the inscribed circle: I[10.5; 5.60550572403]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.731141557° = 137°43'53″ = 0.73877259685 rad
∠ B' = β' = 123.8122065094° = 123°48'43″ = 0.9810664464 rad
∠ C' = γ' = 98.45765193353° = 98°27'23″ = 1.42332022211 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 = 17 ; ; b = 21 ; ; c = 25 ; ;

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

p = a+b+c = 17+21+25 = 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 * (31.5-17)(31.5-21)(31.5-25) } ; ; T = sqrt{ 31173.19 } = 176.56 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 176.56 }{ 17 } = 20.77 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 176.56 }{ 21 } = 16.82 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 176.56 }{ 25 } = 14.12 ; ;

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{ 17**2-21**2-25**2 }{ 2 * 21 * 25 } ) = 42° 16'7" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-17**2-25**2 }{ 2 * 17 * 25 } ) = 56° 11'17" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-17**2-21**2 }{ 2 * 21 * 17 } ) = 81° 32'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 176.56 }{ 31.5 } = 5.61 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 42° 16'7" } = 12.64 ; ;




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