25 28 30 triangle

Acute scalene triangle.

Sides: a = 25   b = 28   c = 30

Area: T = 326.0488213459
Perimeter: p = 83
Semiperimeter: s = 41.5

Angle ∠ A = α = 50.92435231941° = 50°55'25″ = 0.88987831465 rad
Angle ∠ B = β = 60.39661691983° = 60°23'46″ = 1.05441120081 rad
Angle ∠ C = γ = 68.68803076076° = 68°40'49″ = 1.1998697499 rad

Height: ha = 26.08438570767
Height: hb = 23.28991581042
Height: hc = 21.7376547564

Median: ma = 26.18768287503
Median: mb = 23.80112604708
Median: mc = 21.89774884405

Inradius: r = 7.85765834569
Circumradius: R = 16.10219131014

Vertex coordinates: A[30; 0] B[0; 0] C[12.35; 21.7376547564]
Centroid: CG[14.11766666667; 7.24655158547]
Coordinates of the circumscribed circle: U[15; 5.8544195549]
Coordinates of the inscribed circle: I[13.5; 7.85765834569]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 129.0766476806° = 129°4'35″ = 0.88987831465 rad
∠ B' = β' = 119.6043830802° = 119°36'14″ = 1.05441120081 rad
∠ C' = γ' = 111.3219692392° = 111°19'11″ = 1.1998697499 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 = 25 ; ; b = 28 ; ; c = 30 ; ;

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

p = a+b+c = 25+28+30 = 83 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 83 }{ 2 } = 41.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 41.5 * (41.5-25)(41.5-28)(41.5-30) } ; ; T = sqrt{ 106307.44 } = 326.05 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 326.05 }{ 25 } = 26.08 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 326.05 }{ 28 } = 23.29 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 326.05 }{ 30 } = 21.74 ; ;

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{ 25**2-28**2-30**2 }{ 2 * 28 * 30 } ) = 50° 55'25" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-25**2-30**2 }{ 2 * 25 * 30 } ) = 60° 23'46" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-25**2-28**2 }{ 2 * 28 * 25 } ) = 68° 40'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 326.05 }{ 41.5 } = 7.86 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 25 }{ 2 * sin 50° 55'25" } = 16.1 ; ;




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