15 17 25 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 17   c = 25

Area: T = 124.4443511281
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 35.84765565311° = 35°50'48″ = 0.6265640437 rad
Angle ∠ B = β = 41.58325725446° = 41°34'57″ = 0.72657528024 rad
Angle ∠ C = γ = 102.5710870924° = 102°34'15″ = 1.79901994143 rad

Height: ha = 16.59224681708
Height: hb = 14.64404130919
Height: hc = 9.95554809025

Median: ma = 20.01987412192
Median: mb = 18.7821639971
Median: mc = 10.03774299499

Inradius: r = 4.36664389923
Circumradius: R = 12.8077015678

Vertex coordinates: A[25; 0] B[0; 0] C[11.22; 9.95554809025]
Centroid: CG[12.07333333333; 3.31884936342]
Coordinates of the circumscribed circle: U[12.5; -2.78774092946]
Coordinates of the inscribed circle: I[11.5; 4.36664389923]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.1533443469° = 144°9'12″ = 0.6265640437 rad
∠ B' = β' = 138.4177427455° = 138°25'3″ = 0.72657528024 rad
∠ C' = γ' = 77.42991290757° = 77°25'45″ = 1.79901994143 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 = 15 ; ; b = 17 ; ; c = 25 ; ;

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

p = a+b+c = 15+17+25 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-15)(28.5-17)(28.5-25) } ; ; T = sqrt{ 15486.19 } = 124.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 124.44 }{ 15 } = 16.59 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 124.44 }{ 17 } = 14.64 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 124.44 }{ 25 } = 9.96 ; ;

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{ 15**2-17**2-25**2 }{ 2 * 17 * 25 } ) = 35° 50'48" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-15**2-25**2 }{ 2 * 15 * 25 } ) = 41° 34'57" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-15**2-17**2 }{ 2 * 17 * 15 } ) = 102° 34'15" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 124.44 }{ 28.5 } = 4.37 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 35° 50'48" } = 12.81 ; ;




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