12 16 25 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 16   c = 25

Area: T = 77.79441996552
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 22.89904870518° = 22°53'26″ = 0.43995143664 rad
Angle ∠ B = β = 31.24402652162° = 31°14'25″ = 0.54552454872 rad
Angle ∠ C = γ = 125.8699247732° = 125°52'9″ = 2.19768327999 rad

Height: ha = 12.96656999425
Height: hb = 9.72442749569
Height: hc = 6.22435359724

Median: ma = 20.11221853611
Median: mb = 17.903251379
Median: mc = 6.61443782777

Inradius: r = 2.93656301757
Circumradius: R = 15.4255314552

Vertex coordinates: A[25; 0] B[0; 0] C[10.26; 6.22435359724]
Centroid: CG[11.75333333333; 2.07545119908]
Coordinates of the circumscribed circle: U[12.5; -9.03882702453]
Coordinates of the inscribed circle: I[10.5; 2.93656301757]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.1109512948° = 157°6'34″ = 0.43995143664 rad
∠ B' = β' = 148.7659734784° = 148°45'35″ = 0.54552454872 rad
∠ C' = γ' = 54.1310752268° = 54°7'51″ = 2.19768327999 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 = 12 ; ; b = 16 ; ; c = 25 ; ;

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

p = a+b+c = 12+16+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 * (26.5-12)(26.5-16)(26.5-25) } ; ; T = sqrt{ 6051.94 } = 77.79 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 77.79 }{ 12 } = 12.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 77.79 }{ 16 } = 9.72 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 77.79 }{ 25 } = 6.22 ; ;

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{ 12**2-16**2-25**2 }{ 2 * 16 * 25 } ) = 22° 53'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-12**2-25**2 }{ 2 * 12 * 25 } ) = 31° 14'25" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-12**2-16**2 }{ 2 * 16 * 12 } ) = 125° 52'9" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 77.79 }{ 26.5 } = 2.94 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 22° 53'26" } = 15.43 ; ;




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