4 24 25 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 24   c = 25

Area: T = 47.28657007984
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 9.0698721546° = 9°4'7″ = 0.15882790499 rad
Angle ∠ B = β = 71.03444250112° = 71°2'4″ = 1.24397845987 rad
Angle ∠ C = γ = 99.89768534428° = 99°53'49″ = 1.7443529005 rad

Height: ha = 23.64328503992
Height: hb = 3.94404750665
Height: hc = 3.78328560639

Median: ma = 24.42333494836
Median: mb = 13.28553302556
Median: mc = 11.82215904175

Inradius: r = 1.78443660679
Circumradius: R = 12.68988253715

Vertex coordinates: A[25; 0] B[0; 0] C[1.3; 3.78328560639]
Centroid: CG[8.76766666667; 1.26109520213]
Coordinates of the circumscribed circle: U[12.5; -2.18108918607]
Coordinates of the inscribed circle: I[2.5; 1.78443660679]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.9311278454° = 170°55'53″ = 0.15882790499 rad
∠ B' = β' = 108.9665574989° = 108°57'56″ = 1.24397845987 rad
∠ C' = γ' = 80.10331465572° = 80°6'11″ = 1.7443529005 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 = 4 ; ; b = 24 ; ; c = 25 ; ;

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

p = a+b+c = 4+24+25 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-4)(26.5-24)(26.5-25) } ; ; T = sqrt{ 2235.94 } = 47.29 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 47.29 }{ 4 } = 23.64 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 47.29 }{ 24 } = 3.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 47.29 }{ 25 } = 3.78 ; ;

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{ 4**2-24**2-25**2 }{ 2 * 24 * 25 } ) = 9° 4'7" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-4**2-25**2 }{ 2 * 4 * 25 } ) = 71° 2'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-4**2-24**2 }{ 2 * 24 * 4 } ) = 99° 53'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 47.29 }{ 26.5 } = 1.78 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 9° 4'7" } = 12.69 ; ;




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