16 25 27 triangle

Acute scalene triangle.

Sides: a = 16   b = 25   c = 27

Area: T = 196.3576818063
Perimeter: p = 68
Semiperimeter: s = 34

Angle ∠ A = α = 35.57771025511° = 35°34'38″ = 0.62109375778 rad
Angle ∠ B = β = 65.37656816478° = 65°22'32″ = 1.14110208955 rad
Angle ∠ C = γ = 79.04772158011° = 79°2'50″ = 1.38796341803 rad

Height: ha = 24.54546022579
Height: hb = 15.70985454451
Height: hc = 14.54549494862

Median: ma = 24.75988368063
Median: mb = 18.33771208209
Median: mc = 16.077015868

Inradius: r = 5.77552005313
Circumradius: R = 13.75504774554

Vertex coordinates: A[27; 0] B[0; 0] C[6.66766666667; 14.54549494862]
Centroid: CG[11.22222222222; 4.84883164954]
Coordinates of the circumscribed circle: U[13.5; 2.61325907165]
Coordinates of the inscribed circle: I[9; 5.77552005313]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.4232897449° = 144°25'22″ = 0.62109375778 rad
∠ B' = β' = 114.6244318352° = 114°37'28″ = 1.14110208955 rad
∠ C' = γ' = 100.9532784199° = 100°57'10″ = 1.38796341803 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 = 27 ; ;

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

p = a+b+c = 16+25+27 = 68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 68 }{ 2 } = 34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34 * (34-16)(34-25)(34-27) } ; ; T = sqrt{ 38556 } = 196.36 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 196.36 }{ 16 } = 24.54 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 196.36 }{ 25 } = 15.71 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 196.36 }{ 27 } = 14.54 ; ;

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**2-27**2 }{ 2 * 25 * 27 } ) = 35° 34'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-16**2-27**2 }{ 2 * 16 * 27 } ) = 65° 22'32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-16**2-25**2 }{ 2 * 25 * 16 } ) = 79° 2'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 196.36 }{ 34 } = 5.78 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 35° 34'38" } = 13.75 ; ;




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