16 24 25 triangle

Acute scalene triangle.

Sides: a = 16   b = 24   c = 25

Area: T = 184.8944395534
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 38.04875074536° = 38°2'51″ = 0.66440542772 rad
Angle ∠ B = β = 67.58988679538° = 67°35'20″ = 1.18796482835 rad
Angle ∠ C = γ = 74.36436245926° = 74°21'49″ = 1.29878900929 rad

Height: ha = 23.11217994418
Height: hb = 15.40878662945
Height: hc = 14.79215516427

Median: ma = 23.16224696438
Median: mb = 17.21991753577
Median: mc = 16.11767614613

Inradius: r = 5.68990583241
Circumradius: R = 12.9880382629

Vertex coordinates: A[25; 0] B[0; 0] C[6.1; 14.79215516427]
Centroid: CG[10.36766666667; 4.93105172142]
Coordinates of the circumscribed circle: U[12.5; 3.49986187555]
Coordinates of the inscribed circle: I[8.5; 5.68990583241]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.9522492546° = 141°57'9″ = 0.66440542772 rad
∠ B' = β' = 112.4111132046° = 112°24'40″ = 1.18796482835 rad
∠ C' = γ' = 105.6366375407° = 105°38'11″ = 1.29878900929 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 = 16 ; ; b = 24 ; ; c = 25 ; ;

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

p = a+b+c = 16+24+25 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-16)(32.5-24)(32.5-25) } ; ; T = sqrt{ 34185.94 } = 184.89 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 184.89 }{ 16 } = 23.11 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 184.89 }{ 24 } = 15.41 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 184.89 }{ 25 } = 14.79 ; ;

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{ 16**2-24**2-25**2 }{ 2 * 24 * 25 } ) = 38° 2'51" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-16**2-25**2 }{ 2 * 16 * 25 } ) = 67° 35'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-16**2-24**2 }{ 2 * 24 * 16 } ) = 74° 21'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 184.89 }{ 32.5 } = 5.69 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 38° 2'51" } = 12.98 ; ;




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