6 10 14 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 10   c = 14

Area: T = 25.98107621135
Perimeter: p = 30
Semiperimeter: s = 15

Angle ∠ A = α = 21.78767892983° = 21°47'12″ = 0.38802512067 rad
Angle ∠ B = β = 38.21332107017° = 38°12'48″ = 0.66769463445 rad
Angle ∠ C = γ = 120° = 2.09443951024 rad

Height: ha = 8.66602540378
Height: hb = 5.19661524227
Height: hc = 3.71215374448

Median: ma = 11.79898261226
Median: mb = 9.53993920142
Median: mc = 4.35988989435

Inradius: r = 1.73220508076
Circumradius: R = 8.08329037687

Vertex coordinates: A[14; 0] B[0; 0] C[4.71442857143; 3.71215374448]
Centroid: CG[6.23880952381; 1.23771791483]
Coordinates of the circumscribed circle: U[7; -4.04114518843]
Coordinates of the inscribed circle: I[5; 1.73220508076]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.2133210702° = 158°12'48″ = 0.38802512067 rad
∠ B' = β' = 141.7876789298° = 141°47'12″ = 0.66769463445 rad
∠ C' = γ' = 60° = 2.09443951024 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 = 6 ; ; b = 10 ; ; c = 14 ; ;

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

p = a+b+c = 6+10+14 = 30 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 30 }{ 2 } = 15 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 15 * (15-6)(15-10)(15-14) } ; ; T = sqrt{ 675 } = 25.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 25.98 }{ 6 } = 8.66 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 25.98 }{ 10 } = 5.2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 25.98 }{ 14 } = 3.71 ; ;

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{ 6**2-10**2-14**2 }{ 2 * 10 * 14 } ) = 21° 47'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 10**2-6**2-14**2 }{ 2 * 6 * 14 } ) = 38° 12'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14**2-6**2-10**2 }{ 2 * 10 * 6 } ) = 120° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 25.98 }{ 15 } = 1.73 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 21° 47'12" } = 8.08 ; ;




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