8 23 30 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 23   c = 30

Area: T = 50.72990597193
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 8.45554725801° = 8°27'20″ = 0.14875758363 rad
Angle ∠ B = β = 25.00878332347° = 25°28″ = 0.43664690287 rad
Angle ∠ C = γ = 146.5376694185° = 146°32'12″ = 2.55875477885 rad

Height: ha = 12.68222649298
Height: hb = 4.41112225843
Height: hc = 3.38219373146

Median: ma = 26.42991505728
Median: mb = 18.70216042093
Median: mc = 8.45657672626

Inradius: r = 1.66332478596
Circumradius: R = 27.20333427711

Vertex coordinates: A[30; 0] B[0; 0] C[7.25; 3.38219373146]
Centroid: CG[12.41766666667; 1.12773124382]
Coordinates of the circumscribed circle: U[15; -22.69440930183]
Coordinates of the inscribed circle: I[7.5; 1.66332478596]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 171.545452742° = 171°32'40″ = 0.14875758363 rad
∠ B' = β' = 154.9922166765° = 154°59'32″ = 0.43664690287 rad
∠ C' = γ' = 33.46333058148° = 33°27'48″ = 2.55875477885 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 = 8 ; ; b = 23 ; ; c = 30 ; ;

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

p = a+b+c = 8+23+30 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-8)(30.5-23)(30.5-30) } ; ; T = sqrt{ 2573.44 } = 50.73 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 50.73 }{ 8 } = 12.68 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 50.73 }{ 23 } = 4.41 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 50.73 }{ 30 } = 3.38 ; ;

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{ 8**2-23**2-30**2 }{ 2 * 23 * 30 } ) = 8° 27'20" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-8**2-30**2 }{ 2 * 8 * 30 } ) = 25° 28" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-8**2-23**2 }{ 2 * 23 * 8 } ) = 146° 32'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 50.73 }{ 30.5 } = 1.66 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 8° 27'20" } = 27.2 ; ;




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