7 24 30 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 24   c = 30

Area: T = 48.26442466014
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 7.70546928237° = 7°42'17″ = 0.13444722576 rad
Angle ∠ B = β = 27.36551372914° = 27°21'55″ = 0.4787611746 rad
Angle ∠ C = γ = 144.9330169885° = 144°55'49″ = 2.532950865 rad

Height: ha = 13.79897847433
Height: hb = 4.02220205501
Height: hc = 3.21876164401

Median: ma = 26.9439747586
Median: mb = 18.18796589627
Median: mc = 9.35441434669

Inradius: r = 1.58224343148
Circumradius: R = 26.10662813309

Vertex coordinates: A[30; 0] B[0; 0] C[6.21766666667; 3.21876164401]
Centroid: CG[12.07222222222; 1.07325388134]
Coordinates of the circumscribed circle: U[15; -21.36767481131]
Coordinates of the inscribed circle: I[6.5; 1.58224343148]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 172.2955307176° = 172°17'43″ = 0.13444722576 rad
∠ B' = β' = 152.6354862709° = 152°38'5″ = 0.4787611746 rad
∠ C' = γ' = 35.07698301151° = 35°4'11″ = 2.532950865 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 = 7 ; ; b = 24 ; ; c = 30 ; ;

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

p = a+b+c = 7+24+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 * (30.5-7)(30.5-24)(30.5-30) } ; ; T = sqrt{ 2329.44 } = 48.26 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 48.26 }{ 7 } = 13.79 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 48.26 }{ 24 } = 4.02 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 48.26 }{ 30 } = 3.22 ; ;

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{ 7**2-24**2-30**2 }{ 2 * 24 * 30 } ) = 7° 42'17" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-7**2-30**2 }{ 2 * 7 * 30 } ) = 27° 21'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-7**2-24**2 }{ 2 * 24 * 7 } ) = 144° 55'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 48.26 }{ 30.5 } = 1.58 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 7° 42'17" } = 26.11 ; ;




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