5 27 30 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 27   c = 30

Area: T = 56.78802782663
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 8.05993164236° = 8°3'34″ = 0.14106616071 rad
Angle ∠ B = β = 49.20766050518° = 49°12'24″ = 0.85988172719 rad
Angle ∠ C = γ = 122.7344078525° = 122°44'3″ = 2.14221137747 rad

Height: ha = 22.71221113065
Height: hb = 4.20659465382
Height: hc = 3.78553518844

Median: ma = 28.43297379517
Median: mb = 16.74106690428
Median: mc = 12.32988280059

Inradius: r = 1.83216218796
Circumradius: R = 17.83218957024

Vertex coordinates: A[30; 0] B[0; 0] C[3.26766666667; 3.78553518844]
Centroid: CG[11.08988888889; 1.26217839615]
Coordinates of the circumscribed circle: U[15; -9.64224324909]
Coordinates of the inscribed circle: I[4; 1.83216218796]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 171.9410683576° = 171°56'26″ = 0.14106616071 rad
∠ B' = β' = 130.7933394948° = 130°47'36″ = 0.85988172719 rad
∠ C' = γ' = 57.26659214754° = 57°15'57″ = 2.14221137747 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 = 5 ; ; b = 27 ; ; c = 30 ; ;

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

p = a+b+c = 5+27+30 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-5)(31-27)(31-30) } ; ; T = sqrt{ 3224 } = 56.78 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 56.78 }{ 5 } = 22.71 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 56.78 }{ 27 } = 4.21 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 56.78 }{ 30 } = 3.79 ; ;

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{ 5**2-27**2-30**2 }{ 2 * 27 * 30 } ) = 8° 3'34" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-5**2-30**2 }{ 2 * 5 * 30 } ) = 49° 12'24" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-5**2-27**2 }{ 2 * 27 * 5 } ) = 122° 44'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 56.78 }{ 31 } = 1.83 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 8° 3'34" } = 17.83 ; ;




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