14 24 25 triangle

Acute scalene triangle.

Sides: a = 14   b = 24   c = 25

Area: T = 163.9311197458
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 33.12329402077° = 33°7'23″ = 0.57881043646 rad
Angle ∠ B = β = 69.51326848853° = 69°30'46″ = 1.21332252231 rad
Angle ∠ C = γ = 77.3644374907° = 77°21'52″ = 1.35502630659 rad

Height: ha = 23.4198742494
Height: hb = 13.66109331215
Height: hc = 13.11444957966

Median: ma = 23.48440371316
Median: mb = 16.32548277173
Median: mc = 15.15875063912

Inradius: r = 5.20441649987
Circumradius: R = 12.81102523044

Vertex coordinates: A[25; 0] B[0; 0] C[4.9; 13.11444957966]
Centroid: CG[9.96766666667; 4.37114985989]
Coordinates of the circumscribed circle: U[12.5; 2.80222426916]
Coordinates of the inscribed circle: I[7.5; 5.20441649987]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.8777059792° = 146°52'37″ = 0.57881043646 rad
∠ B' = β' = 110.4877315115° = 110°29'14″ = 1.21332252231 rad
∠ C' = γ' = 102.6365625093° = 102°38'8″ = 1.35502630659 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 = 14 ; ; b = 24 ; ; c = 25 ; ;

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

p = a+b+c = 14+24+25 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-14)(31.5-24)(31.5-25) } ; ; T = sqrt{ 26873.44 } = 163.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 163.93 }{ 14 } = 23.42 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 163.93 }{ 24 } = 13.66 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 163.93 }{ 25 } = 13.11 ; ;

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{ 14**2-24**2-25**2 }{ 2 * 24 * 25 } ) = 33° 7'23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-14**2-25**2 }{ 2 * 14 * 25 } ) = 69° 30'46" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-14**2-24**2 }{ 2 * 24 * 14 } ) = 77° 21'52" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 163.93 }{ 31.5 } = 5.2 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 33° 7'23" } = 12.81 ; ;




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