15.5 12.7 3.2 triangle

Obtuse scalene triangle.

Sides: a = 15.5   b = 12.7   c = 3.2

Area: T = 10.85112672071
Perimeter: p = 31.4
Semiperimeter: s = 15.7

Angle ∠ A = α = 147.7232589398° = 147°43'21″ = 2.57882455646 rad
Angle ∠ B = β = 25.94877355847° = 25°56'52″ = 0.45328734194 rad
Angle ∠ C = γ = 6.33296750172° = 6°19'47″ = 0.11104736696 rad

Height: ha = 1.44001635106
Height: hb = 1.70988609775
Height: hc = 6.78220420044

Median: ma = 5.07697633081
Median: mb = 9.21553404712
Median: mc = 14.0798707327

Inradius: r = 0.69111635164
Circumradius: R = 14.51325907412

Vertex coordinates: A[3.2; 0] B[0; 0] C[13.93875; 6.78220420044]
Centroid: CG[5.71325; 2.26106806681]
Coordinates of the circumscribed circle: U[1.6; 14.42441218111]
Coordinates of the inscribed circle: I[3; 0.69111635164]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 32.27774106019° = 32°16'39″ = 2.57882455646 rad
∠ B' = β' = 154.0522264415° = 154°3'8″ = 0.45328734194 rad
∠ C' = γ' = 173.6770324983° = 173°40'13″ = 0.11104736696 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 = 15.5 ; ; b = 12.7 ; ; c = 3.2 ; ;

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

p = a+b+c = 15.5+12.7+3.2 = 31.4 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 31.4 }{ 2 } = 15.7 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 15.7 * (15.7-15.5)(15.7-12.7)(15.7-3.2) } ; ; T = sqrt{ 117.75 } = 10.85 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 10.85 }{ 15.5 } = 1.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 10.85 }{ 12.7 } = 1.71 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 10.85 }{ 3.2 } = 6.78 ; ;

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{ 15.5**2-12.7**2-3.2**2 }{ 2 * 12.7 * 3.2 } ) = 147° 43'21" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12.7**2-15.5**2-3.2**2 }{ 2 * 15.5 * 3.2 } ) = 25° 56'52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 3.2**2-15.5**2-12.7**2 }{ 2 * 12.7 * 15.5 } ) = 6° 19'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 10.85 }{ 15.7 } = 0.69 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15.5 }{ 2 * sin 147° 43'21" } = 14.51 ; ;




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