17 25 30 triangle

Acute scalene triangle.

Sides: a = 17   b = 25   c = 30

Area: T = 212.4711174515
Perimeter: p = 72
Semiperimeter: s = 36

Angle ∠ A = α = 34.5132762755° = 34°30'46″ = 0.6022361344 rad
Angle ∠ B = β = 56.43109751098° = 56°25'52″ = 0.98549063158 rad
Angle ∠ C = γ = 89.05662621352° = 89°3'23″ = 1.55443249938 rad

Height: ha = 24.99766087665
Height: hb = 16.99876939612
Height: hc = 14.16547449677

Median: ma = 26.27326093108
Median: mb = 20.93444214155
Median: mc = 15.23215462117

Inradius: r = 5.90219770699
Circumradius: R = 15.00220350161

Vertex coordinates: A[30; 0] B[0; 0] C[9.4; 14.16547449677]
Centroid: CG[13.13333333333; 4.72215816559]
Coordinates of the circumscribed circle: U[15; 0.24770923414]
Coordinates of the inscribed circle: I[11; 5.90219770699]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.4877237245° = 145°29'14″ = 0.6022361344 rad
∠ B' = β' = 123.569902489° = 123°34'8″ = 0.98549063158 rad
∠ C' = γ' = 90.94437378648° = 90°56'37″ = 1.55443249938 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 = 25 ; ; c = 30 ; ;

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

p = a+b+c = 17+25+30 = 72 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 72 }{ 2 } = 36 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36 * (36-17)(36-25)(36-30) } ; ; T = sqrt{ 45144 } = 212.47 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 212.47 }{ 17 } = 25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 212.47 }{ 25 } = 17 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 212.47 }{ 30 } = 14.16 ; ;

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**2-25**2-30**2 }{ 2 * 25 * 30 } ) = 34° 30'46" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-17**2-30**2 }{ 2 * 17 * 30 } ) = 56° 25'52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-17**2-25**2 }{ 2 * 25 * 17 } ) = 89° 3'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 212.47 }{ 36 } = 5.9 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 34° 30'46" } = 15 ; ;




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