2 24 25 triangle

Obtuse scalene triangle.

Sides: a = 2   b = 24   c = 25

Area: T = 21.21999410377
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 4.05222679444° = 4°3'8″ = 0.07107254178 rad
Angle ∠ B = β = 57.99545451722° = 57°59'40″ = 1.01221957615 rad
Angle ∠ C = γ = 117.9533186883° = 117°57'11″ = 2.05986714743 rad

Height: ha = 21.21999410377
Height: hb = 1.76766617531
Height: hc = 1.6965995283

Median: ma = 24.48546890934
Median: mb = 13.05875648572
Median: mc = 11.56550335062

Inradius: r = 0.83113702368
Circumradius: R = 14.15109827535

Vertex coordinates: A[25; 0] B[0; 0] C[1.06; 1.6965995283]
Centroid: CG[8.68766666667; 0.5655331761]
Coordinates of the circumscribed circle: U[12.5; -6.63332731657]
Coordinates of the inscribed circle: I[1.5; 0.83113702368]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 175.9487732056° = 175°56'52″ = 0.07107254178 rad
∠ B' = β' = 122.0055454828° = 122°20″ = 1.01221957615 rad
∠ C' = γ' = 62.04768131166° = 62°2'49″ = 2.05986714743 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 = 2 ; ; b = 24 ; ; c = 25 ; ;

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

p = a+b+c = 2+24+25 = 51 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 51 }{ 2 } = 25.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25.5 * (25.5-2)(25.5-24)(25.5-25) } ; ; T = sqrt{ 449.44 } = 21.2 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 21.2 }{ 2 } = 21.2 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 21.2 }{ 24 } = 1.77 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 21.2 }{ 25 } = 1.7 ; ;

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{ 2**2-24**2-25**2 }{ 2 * 24 * 25 } ) = 4° 3'8" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-2**2-25**2 }{ 2 * 2 * 25 } ) = 57° 59'40" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-2**2-24**2 }{ 2 * 24 * 2 } ) = 117° 57'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 21.2 }{ 25.5 } = 0.83 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 4° 3'8" } = 14.15 ; ;




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