24 28 30 triangle

Acute scalene triangle.

Sides: a = 24   b = 28   c = 30

Area: T = 315.7077142776
Perimeter: p = 82
Semiperimeter: s = 41

Angle ∠ A = α = 48.73664340939° = 48°44'11″ = 0.85106112406 rad
Angle ∠ B = β = 61.27883074912° = 61°16'42″ = 1.07695082258 rad
Angle ∠ C = γ = 69.98552584149° = 69°59'7″ = 1.22114731872 rad

Height: ha = 26.30989285647
Height: hb = 22.55105101983
Height: hc = 21.04771428518

Median: ma = 26.42196896272
Median: mb = 23.28108934536
Median: mc = 21.33107290077

Inradius: r = 7.77001742141
Circumradius: R = 15.96441620892

Vertex coordinates: A[30; 0] B[0; 0] C[11.53333333333; 21.04771428518]
Centroid: CG[13.84444444444; 7.01657142839]
Coordinates of the circumscribed circle: U[15; 5.46439245246]
Coordinates of the inscribed circle: I[13; 7.77001742141]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 131.2643565906° = 131°15'49″ = 0.85106112406 rad
∠ B' = β' = 118.7221692509° = 118°43'18″ = 1.07695082258 rad
∠ C' = γ' = 110.0154741585° = 110°53″ = 1.22114731872 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 = 24 ; ; b = 28 ; ; c = 30 ; ;

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

p = a+b+c = 24+28+30 = 82 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 82 }{ 2 } = 41 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 41 * (41-24)(41-28)(41-30) } ; ; T = sqrt{ 99671 } = 315.71 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 315.71 }{ 24 } = 26.31 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 315.71 }{ 28 } = 22.55 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 315.71 }{ 30 } = 21.05 ; ;

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{ 24**2-28**2-30**2 }{ 2 * 28 * 30 } ) = 48° 44'11" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-24**2-30**2 }{ 2 * 24 * 30 } ) = 61° 16'42" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-24**2-28**2 }{ 2 * 28 * 24 } ) = 69° 59'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 315.71 }{ 41 } = 7.7 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 24 }{ 2 * sin 48° 44'11" } = 15.96 ; ;




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