15 25 30 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 25   c = 30

Area: T = 187.0832869339
Perimeter: p = 70
Semiperimeter: s = 35

Angle ∠ A = α = 29.92664348666° = 29°55'35″ = 0.52223148218 rad
Angle ∠ B = β = 56.25110114041° = 56°15'4″ = 0.98217653566 rad
Angle ∠ C = γ = 93.82325537293° = 93°49'21″ = 1.63875124752 rad

Height: ha = 24.94443825785
Height: hb = 14.96766295471
Height: hc = 12.47221912892

Median: ma = 26.57553645318
Median: mb = 20.15656443707
Median: mc = 14.14221356237

Inradius: r = 5.34552248382
Circumradius: R = 15.03334448576

Vertex coordinates: A[30; 0] B[0; 0] C[8.33333333333; 12.47221912892]
Centroid: CG[12.77877777778; 4.15773970964]
Coordinates of the circumscribed circle: U[15; -1.00222296572]
Coordinates of the inscribed circle: I[10; 5.34552248382]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.0743565133° = 150°4'25″ = 0.52223148218 rad
∠ B' = β' = 123.7498988596° = 123°44'56″ = 0.98217653566 rad
∠ C' = γ' = 86.17774462707° = 86°10'39″ = 1.63875124752 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 = 25 ; ; c = 30 ; ;

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

p = a+b+c = 15+25+30 = 70 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 70 }{ 2 } = 35 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35 * (35-15)(35-25)(35-30) } ; ; T = sqrt{ 35000 } = 187.08 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 187.08 }{ 15 } = 24.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 187.08 }{ 25 } = 14.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 187.08 }{ 30 } = 12.47 ; ;

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**2-25**2-30**2 }{ 2 * 25 * 30 } ) = 29° 55'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-15**2-30**2 }{ 2 * 15 * 30 } ) = 56° 15'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-15**2-25**2 }{ 2 * 25 * 15 } ) = 93° 49'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 187.08 }{ 35 } = 5.35 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 29° 55'35" } = 15.03 ; ;




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