18 28 30 triangle

Acute scalene triangle.

Sides: a = 18   b = 28   c = 30

Area: T = 246.5776560119
Perimeter: p = 76
Semiperimeter: s = 38

Angle ∠ A = α = 35.95105676196° = 35°57'2″ = 0.62774557729 rad
Angle ∠ B = β = 65.95879240942° = 65°57'29″ = 1.15111829432 rad
Angle ∠ C = γ = 78.09215082861° = 78°5'29″ = 1.36329539374 rad

Height: ha = 27.39773955688
Height: hb = 17.61326114371
Height: hc = 16.43884373413

Median: ma = 27.58662284483
Median: mb = 20.39660780544
Median: mc = 18.13883571472

Inradius: r = 6.48988568452
Circumradius: R = 15.33299242969

Vertex coordinates: A[30; 0] B[0; 0] C[7.33333333333; 16.43884373413]
Centroid: CG[12.44444444444; 5.47994791138]
Coordinates of the circumscribed circle: U[15; 3.1633317712]
Coordinates of the inscribed circle: I[10; 6.48988568452]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.049943238° = 144°2'58″ = 0.62774557729 rad
∠ B' = β' = 114.0422075906° = 114°2'31″ = 1.15111829432 rad
∠ C' = γ' = 101.9088491714° = 101°54'31″ = 1.36329539374 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 = 18 ; ; b = 28 ; ; c = 30 ; ;

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

p = a+b+c = 18+28+30 = 76 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 76 }{ 2 } = 38 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 38 * (38-18)(38-28)(38-30) } ; ; T = sqrt{ 60800 } = 246.58 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 246.58 }{ 18 } = 27.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 246.58 }{ 28 } = 17.61 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 246.58 }{ 30 } = 16.44 ; ;

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{ 18**2-28**2-30**2 }{ 2 * 28 * 30 } ) = 35° 57'2" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-18**2-30**2 }{ 2 * 18 * 30 } ) = 65° 57'29" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-18**2-28**2 }{ 2 * 28 * 18 } ) = 78° 5'29" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 246.58 }{ 38 } = 6.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 35° 57'2" } = 15.33 ; ;




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