16 25 28 triangle

Acute scalene triangle.

Sides: a = 16   b = 25   c = 28

Area: T = 198.5244400264
Perimeter: p = 69
Semiperimeter: s = 34.5

Angle ∠ A = α = 34.55660777693° = 34°33'22″ = 0.60331173336 rad
Angle ∠ B = β = 62.40881713429° = 62°24'29″ = 1.08992280701 rad
Angle ∠ C = γ = 83.03657508879° = 83°2'9″ = 1.44992472499 rad

Height: ha = 24.81655500329
Height: hb = 15.88219520211
Height: hc = 14.18803143045

Median: ma = 25.30881014697
Median: mb = 19.07222311228
Median: mc = 15.63664957711

Inradius: r = 5.75443304424
Circumradius: R = 14.10440597341

Vertex coordinates: A[28; 0] B[0; 0] C[7.41107142857; 14.18803143045]
Centroid: CG[11.80435714286; 4.72767714348]
Coordinates of the circumscribed circle: U[14; 1.71101172428]
Coordinates of the inscribed circle: I[9.5; 5.75443304424]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.4443922231° = 145°26'38″ = 0.60331173336 rad
∠ B' = β' = 117.5921828657° = 117°35'31″ = 1.08992280701 rad
∠ C' = γ' = 96.96442491121° = 96°57'51″ = 1.44992472499 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 = 28 ; ;

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

p = a+b+c = 16+25+28 = 69 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 69 }{ 2 } = 34.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34.5 * (34.5-16)(34.5-25)(34.5-28) } ; ; T = sqrt{ 39411.94 } = 198.52 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 198.52 }{ 16 } = 24.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 198.52 }{ 25 } = 15.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 198.52 }{ 28 } = 14.18 ; ;

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**2-28**2 }{ 2 * 25 * 28 } ) = 34° 33'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-16**2-28**2 }{ 2 * 16 * 28 } ) = 62° 24'29" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-16**2-25**2 }{ 2 * 25 * 16 } ) = 83° 2'9" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 198.52 }{ 34.5 } = 5.75 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 34° 33'22" } = 14.1 ; ;




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