8 24 25 triangle

Acute scalene triangle.

Sides: a = 8   b = 24   c = 25

Area: T = 95.92767298515
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 18.64881553056° = 18°38'53″ = 0.32554717095 rad
Angle ∠ B = β = 73.59105306552° = 73°35'26″ = 1.28443970582 rad
Angle ∠ C = γ = 87.76113140392° = 87°45'41″ = 1.53217238859 rad

Height: ha = 23.98216824629
Height: hb = 7.99438941543
Height: hc = 7.67441383881

Median: ma = 24.17664348075
Median: mb = 14.16598022585
Median: mc = 12.79664838921

Inradius: r = 3.36658501702
Circumradius: R = 12.5109547671

Vertex coordinates: A[25; 0] B[0; 0] C[2.26; 7.67441383881]
Centroid: CG[9.08766666667; 2.55880461294]
Coordinates of the circumscribed circle: U[12.5; 0.48986542059]
Coordinates of the inscribed circle: I[4.5; 3.36658501702]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.3521844694° = 161°21'7″ = 0.32554717095 rad
∠ B' = β' = 106.4099469345° = 106°24'34″ = 1.28443970582 rad
∠ C' = γ' = 92.23986859608° = 92°14'19″ = 1.53217238859 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 = 8 ; ; b = 24 ; ; c = 25 ; ;

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

p = a+b+c = 8+24+25 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-8)(28.5-24)(28.5-25) } ; ; T = sqrt{ 9201.94 } = 95.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 95.93 }{ 8 } = 23.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 95.93 }{ 24 } = 7.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 95.93 }{ 25 } = 7.67 ; ;

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{ 8**2-24**2-25**2 }{ 2 * 24 * 25 } ) = 18° 38'53" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-8**2-25**2 }{ 2 * 8 * 25 } ) = 73° 35'26" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-8**2-24**2 }{ 2 * 24 * 8 } ) = 87° 45'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 95.93 }{ 28.5 } = 3.37 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 18° 38'53" } = 12.51 ; ;




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