7 14 16 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 14   c = 16

Area: T = 48.92327707719
Perimeter: p = 37
Semiperimeter: s = 18.5

Angle ∠ A = α = 25.90105519005° = 25°54'2″ = 0.45220499087 rad
Angle ∠ B = β = 60.88221782058° = 60°52'56″ = 1.06325944655 rad
Angle ∠ C = γ = 93.21772698937° = 93°13'2″ = 1.62769482794 rad

Height: ha = 13.97879345063
Height: hb = 6.98989672531
Height: hc = 6.11553463465

Median: ma = 14.62201915172
Median: mb = 10.17334949747
Median: mc = 7.64985292704

Inradius: r = 2.64444740958
Circumradius: R = 8.01326287578

Vertex coordinates: A[16; 0] B[0; 0] C[3.406625; 6.11553463465]
Centroid: CG[6.469875; 2.03884487822]
Coordinates of the circumscribed circle: U[8; -0.45496883487]
Coordinates of the inscribed circle: I[4.5; 2.64444740958]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.0999448099° = 154°5'58″ = 0.45220499087 rad
∠ B' = β' = 119.1187821794° = 119°7'4″ = 1.06325944655 rad
∠ C' = γ' = 86.78327301063° = 86°46'58″ = 1.62769482794 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 = 7 ; ; b = 14 ; ; c = 16 ; ;

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

p = a+b+c = 7+14+16 = 37 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 37 }{ 2 } = 18.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18.5 * (18.5-7)(18.5-14)(18.5-16) } ; ; T = sqrt{ 2393.44 } = 48.92 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 48.92 }{ 7 } = 13.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 48.92 }{ 14 } = 6.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 48.92 }{ 16 } = 6.12 ; ;

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{ 7**2-14**2-16**2 }{ 2 * 14 * 16 } ) = 25° 54'2" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-7**2-16**2 }{ 2 * 7 * 16 } ) = 60° 52'56" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-7**2-14**2 }{ 2 * 14 * 7 } ) = 93° 13'2" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 48.92 }{ 18.5 } = 2.64 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 25° 54'2" } = 8.01 ; ;




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