16 25 30 triangle

Obtuse scalene triangle.

Sides: a = 16   b = 25   c = 30

Area: T = 199.9443585794
Perimeter: p = 71
Semiperimeter: s = 35.5

Angle ∠ A = α = 32.22107635824° = 32°13'15″ = 0.5622358412 rad
Angle ∠ B = β = 56.41883336947° = 56°25'6″ = 0.98546856815 rad
Angle ∠ C = γ = 91.36109027229° = 91°21'39″ = 1.59545485601 rad

Height: ha = 24.99329482242
Height: hb = 15.99554868635
Height: hc = 13.33295723862

Median: ma = 26.42991505728
Median: mb = 20.53765527779
Median: mc = 14.68799182559

Inradius: r = 5.63222136843
Circumradius: R = 15.00442322593

Vertex coordinates: A[30; 0] B[0; 0] C[8.85; 13.33295723862]
Centroid: CG[12.95; 4.44331907954]
Coordinates of the circumscribed circle: U[15; -0.35663505162]
Coordinates of the inscribed circle: I[10.5; 5.63222136843]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.7799236418° = 147°46'45″ = 0.5622358412 rad
∠ B' = β' = 123.5821666305° = 123°34'54″ = 0.98546856815 rad
∠ C' = γ' = 88.63990972771° = 88°38'21″ = 1.59545485601 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 = 25 ; ; c = 30 ; ;

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

p = a+b+c = 16+25+30 = 71 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 71 }{ 2 } = 35.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35.5 * (35.5-16)(35.5-25)(35.5-30) } ; ; T = sqrt{ 39977.44 } = 199.94 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 199.94 }{ 16 } = 24.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 199.94 }{ 25 } = 16 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 199.94 }{ 30 } = 13.33 ; ;

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**2-25**2-30**2 }{ 2 * 25 * 30 } ) = 32° 13'15" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-16**2-30**2 }{ 2 * 16 * 30 } ) = 56° 25'6" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-16**2-25**2 }{ 2 * 25 * 16 } ) = 91° 21'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 199.94 }{ 35.5 } = 5.63 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 32° 13'15" } = 15 ; ;




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