7 24 28 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 24   c = 28

Area: T = 743.9995777015
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 12.72329440288° = 12°43'23″ = 0.22220572638 rad
Angle ∠ B = β = 49.03439100783° = 49°2'2″ = 0.8565803176 rad
Angle ∠ C = γ = 118.2433145893° = 118°14'35″ = 2.06437322137 rad

Height: ha = 21.14327364861
Height: hb = 6.16766314751
Height: hc = 5.28656841215

Median: ma = 25.84108591188
Median: mb = 16.50875740192
Median: mc = 10.79435165725

Inradius: r = 2.50884602611
Circumradius: R = 15.89219825832

Vertex coordinates: A[28; 0] B[0; 0] C[4.58992857143; 5.28656841215]
Centroid: CG[10.86330952381; 1.76218947072]
Coordinates of the circumscribed circle: U[14; -7.52203131867]
Coordinates of the inscribed circle: I[5.5; 2.50884602611]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.2777055971° = 167°16'37″ = 0.22220572638 rad
∠ B' = β' = 130.9666089922° = 130°57'58″ = 0.8565803176 rad
∠ C' = γ' = 61.75768541071° = 61°45'25″ = 2.06437322137 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 = 28 ; ;

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

p = a+b+c = 7+24+28 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-7)(29.5-24)(29.5-28) } ; ; T = sqrt{ 5475.94 } = 74 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 74 }{ 7 } = 21.14 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 74 }{ 24 } = 6.17 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 74 }{ 28 } = 5.29 ; ;

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{ 7**2-24**2-28**2 }{ 2 * 24 * 28 } ) = 12° 43'23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-7**2-28**2 }{ 2 * 7 * 28 } ) = 49° 2'2" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-7**2-24**2 }{ 2 * 24 * 7 } ) = 118° 14'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 74 }{ 29.5 } = 2.51 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 12° 43'23" } = 15.89 ; ;




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