5 29 30 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 29   c = 30

Area: T = 72
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 9.52772833815° = 9°31'38″ = 0.16662824638 rad
Angle ∠ B = β = 73.74397952917° = 73°44'23″ = 1.28770022176 rad
Angle ∠ C = γ = 96.73329213269° = 96°43'59″ = 1.68883079722 rad

Height: ha = 28.8
Height: hb = 4.96655172414
Height: hc = 4.8

Median: ma = 29.39881291922
Median: mb = 15.88223801743
Median: mc = 14.42222051019

Inradius: r = 2.25
Circumradius: R = 15.10441666667

Vertex coordinates: A[30; 0] B[0; 0] C[1.4; 4.8]
Centroid: CG[10.46766666667; 1.6]
Coordinates of the circumscribed circle: U[15; -1.77108333333]
Coordinates of the inscribed circle: I[3; 2.25]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.4732716619° = 170°28'22″ = 0.16662824638 rad
∠ B' = β' = 106.2660204708° = 106°15'37″ = 1.28770022176 rad
∠ C' = γ' = 83.26770786731° = 83°16'1″ = 1.68883079722 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 = 29 ; ; c = 30 ; ;

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

p = a+b+c = 5+29+30 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-5)(32-29)(32-30) } ; ; T = sqrt{ 5184 } = 72 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 72 }{ 5 } = 28.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 72 }{ 29 } = 4.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 72 }{ 30 } = 4.8 ; ;

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**2-29**2-30**2 }{ 2 * 29 * 30 } ) = 9° 31'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-5**2-30**2 }{ 2 * 5 * 30 } ) = 73° 44'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-5**2-29**2 }{ 2 * 29 * 5 } ) = 96° 43'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 72 }{ 32 } = 2.25 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 9° 31'38" } = 15.1 ; ;




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