18 24 28 triangle

Acute scalene triangle.

Sides: a = 18   b = 24   c = 28

Area: T = 214.044438792
Perimeter: p = 70
Semiperimeter: s = 35

Angle ∠ A = α = 39.57112194572° = 39°34'16″ = 0.69106480686 rad
Angle ∠ B = β = 58.1454569176° = 58°8'40″ = 1.01548141743 rad
Angle ∠ C = γ = 82.28442113668° = 82°17'3″ = 1.43661304108 rad

Height: ha = 23.78327097689
Height: hb = 17.83770323267
Height: hc = 15.28988848514

Median: ma = 24.4744476501
Median: mb = 20.24884567313
Median: mc = 15.93773774505

Inradius: r = 6.11655539406
Circumradius: R = 14.12879107076

Vertex coordinates: A[28; 0] B[0; 0] C[9.5; 15.28988848514]
Centroid: CG[12.5; 5.09662949505]
Coordinates of the circumscribed circle: U[14; 1.89768028265]
Coordinates of the inscribed circle: I[11; 6.11655539406]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.4298780543° = 140°25'44″ = 0.69106480686 rad
∠ B' = β' = 121.8555430824° = 121°51'20″ = 1.01548141743 rad
∠ C' = γ' = 97.71657886332° = 97°42'57″ = 1.43661304108 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 = 24 ; ; c = 28 ; ;

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

p = a+b+c = 18+24+28 = 70 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 70 }{ 2 } = 35 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35 * (35-18)(35-24)(35-28) } ; ; T = sqrt{ 45815 } = 214.04 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 214.04 }{ 18 } = 23.78 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 214.04 }{ 24 } = 17.84 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 214.04 }{ 28 } = 15.29 ; ;

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**2-24**2-28**2 }{ 2 * 24 * 28 } ) = 39° 34'16" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-18**2-28**2 }{ 2 * 18 * 28 } ) = 58° 8'40" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-18**2-24**2 }{ 2 * 24 * 18 } ) = 82° 17'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 214.04 }{ 35 } = 6.12 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 39° 34'16" } = 14.13 ; ;




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