17 20 25 triangle

Acute scalene triangle.

Sides: a = 17   b = 20   c = 25

Area: T = 169.2455383984
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 42.60882175298° = 42°36'30″ = 0.74436536843 rad
Angle ∠ B = β = 52.79223196383° = 52°47'32″ = 0.92113997975 rad
Angle ∠ C = γ = 84.59994628319° = 84°35'58″ = 1.47765391718 rad

Height: ha = 19.91112216452
Height: hb = 16.92545383984
Height: hc = 13.54396307187

Median: ma = 20.98221352584
Median: mb = 18.89444436277
Median: mc = 13.7220422734

Inradius: r = 5.46595285156
Circumradius: R = 12.55657338698

Vertex coordinates: A[25; 0] B[0; 0] C[10.28; 13.54396307187]
Centroid: CG[11.76; 4.51332102396]
Coordinates of the circumscribed circle: U[12.5; 1.18217161289]
Coordinates of the inscribed circle: I[11; 5.46595285156]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.392178247° = 137°23'30″ = 0.74436536843 rad
∠ B' = β' = 127.2087680362° = 127°12'28″ = 0.92113997975 rad
∠ C' = γ' = 95.40105371681° = 95°24'2″ = 1.47765391718 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 = 20 ; ; c = 25 ; ;

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

p = a+b+c = 17+20+25 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-17)(31-20)(31-25) } ; ; T = sqrt{ 28644 } = 169.25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 169.25 }{ 17 } = 19.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 169.25 }{ 20 } = 16.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 169.25 }{ 25 } = 13.54 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 20**2+25**2-17**2 }{ 2 * 20 * 25 } ) = 42° 36'30" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 17**2+25**2-20**2 }{ 2 * 17 * 25 } ) = 52° 47'32" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 17**2+20**2-25**2 }{ 2 * 17 * 20 } ) = 84° 35'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 169.25 }{ 31 } = 5.46 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 42° 36'30" } = 12.56 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 20**2+2 * 25**2 - 17**2 } }{ 2 } = 20.982 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 25**2+2 * 17**2 - 20**2 } }{ 2 } = 18.894 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 20**2+2 * 17**2 - 25**2 } }{ 2 } = 13.72 ; ;
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