17 22 25 triangle

Acute scalene triangle.

Sides: a = 17   b = 22   c = 25

Area: T = 183.3033027798
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 41.80218441931° = 41°48'7″ = 0.73295798146 rad
Angle ∠ B = β = 59.61100575507° = 59°36'36″ = 1.04403917716 rad
Angle ∠ C = γ = 78.58880982562° = 78°35'17″ = 1.37216210675 rad

Height: ha = 21.56550620939
Height: hb = 16.6643911618
Height: hc = 14.66442422239

Median: ma = 21.9660191256
Median: mb = 18.33303027798
Median: mc = 15.17439909055

Inradius: r = 5.72882196187
Circumradius: R = 12.75221079607

Vertex coordinates: A[25; 0] B[0; 0] C[8.6; 14.66442422239]
Centroid: CG[11.2; 4.88880807413]
Coordinates of the circumscribed circle: U[12.5; 2.52331443559]
Coordinates of the inscribed circle: I[10; 5.72882196187]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.1988155807° = 138°11'53″ = 0.73295798146 rad
∠ B' = β' = 120.3989942449° = 120°23'24″ = 1.04403917716 rad
∠ C' = γ' = 101.4121901744° = 101°24'43″ = 1.37216210675 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 = 22 ; ; c = 25 ; ;

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

p = a+b+c = 17+22+25 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-17)(32-22)(32-25) } ; ; T = sqrt{ 33600 } = 183.3 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 183.3 }{ 17 } = 21.57 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 183.3 }{ 22 } = 16.66 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 183.3 }{ 25 } = 14.66 ; ;

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**2-22**2-25**2 }{ 2 * 22 * 25 } ) = 41° 48'7" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-17**2-25**2 }{ 2 * 17 * 25 } ) = 59° 36'36" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-17**2-22**2 }{ 2 * 22 * 17 } ) = 78° 35'17" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 183.3 }{ 32 } = 5.73 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 41° 48'7" } = 12.75 ; ;




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