15 20 30 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 20   c = 30

Area: T = 133.3177056298
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 26.38443297494° = 26°23'4″ = 0.46604934251 rad
Angle ∠ B = β = 36.33660575146° = 36°20'10″ = 0.63441838408 rad
Angle ∠ C = γ = 117.2879612736° = 117°16'47″ = 2.04769153877 rad

Height: ha = 17.77656075064
Height: hb = 13.33217056298
Height: hc = 8.88878037532

Median: ma = 24.3676985862
Median: mb = 21.50658131676
Median: mc = 9.35441434669

Inradius: r = 4.10220632707
Circumradius: R = 16.87770603138

Vertex coordinates: A[30; 0] B[0; 0] C[12.08333333333; 8.88878037532]
Centroid: CG[14.02877777778; 2.96326012511]
Coordinates of the circumscribed circle: U[15; -7.73553193105]
Coordinates of the inscribed circle: I[12.5; 4.10220632707]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.6165670251° = 153°36'56″ = 0.46604934251 rad
∠ B' = β' = 143.6643942485° = 143°39'50″ = 0.63441838408 rad
∠ C' = γ' = 62.7220387264° = 62°43'13″ = 2.04769153877 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 = 20 ; ; c = 30 ; ;

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

p = a+b+c = 15+20+30 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-15)(32.5-20)(32.5-30) } ; ; T = sqrt{ 17773.44 } = 133.32 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 133.32 }{ 15 } = 17.78 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 133.32 }{ 20 } = 13.33 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 133.32 }{ 30 } = 8.89 ; ;

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**2-20**2-30**2 }{ 2 * 20 * 30 } ) = 26° 23'4" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-15**2-30**2 }{ 2 * 15 * 30 } ) = 36° 20'10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-15**2-20**2 }{ 2 * 20 * 15 } ) = 117° 16'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 133.32 }{ 32.5 } = 4.1 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 26° 23'4" } = 16.88 ; ;




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