15 22 30 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 22   c = 30

Area: T = 157.9439664113
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 28.59443347318° = 28°35'40″ = 0.49990652885 rad
Angle ∠ B = β = 44.58439897257° = 44°35'2″ = 0.77881374144 rad
Angle ∠ C = γ = 106.8221675543° = 106°49'18″ = 1.86443899507 rad

Height: ha = 21.05986218817
Height: hb = 14.3588151283
Height: hc = 10.52993109408

Median: ma = 25.21440833662
Median: mb = 21.01219013895
Median: mc = 11.38798066767

Inradius: r = 4.71546168392
Circumradius: R = 15.6710541114

Vertex coordinates: A[30; 0] B[0; 0] C[10.68333333333; 10.52993109408]
Centroid: CG[13.56111111111; 3.51097703136]
Coordinates of the circumscribed circle: U[15; -4.53549596254]
Coordinates of the inscribed circle: I[11.5; 4.71546168392]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.4065665268° = 151°24'20″ = 0.49990652885 rad
∠ B' = β' = 135.4166010274° = 135°24'58″ = 0.77881374144 rad
∠ C' = γ' = 73.17883244575° = 73°10'42″ = 1.86443899507 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 = 22 ; ; c = 30 ; ;

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

p = a+b+c = 15+22+30 = 67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67 }{ 2 } = 33.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.5 * (33.5-15)(33.5-22)(33.5-30) } ; ; T = sqrt{ 24944.94 } = 157.94 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 157.94 }{ 15 } = 21.06 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 157.94 }{ 22 } = 14.36 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 157.94 }{ 30 } = 10.53 ; ;

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**2-22**2-30**2 }{ 2 * 22 * 30 } ) = 28° 35'40" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-15**2-30**2 }{ 2 * 15 * 30 } ) = 44° 35'2" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-15**2-22**2 }{ 2 * 22 * 15 } ) = 106° 49'18" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 157.94 }{ 33.5 } = 4.71 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 28° 35'40" } = 15.67 ; ;




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