7 12 14 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 12   c = 14

Area: T = 41.99333030375
Perimeter: p = 33
Semiperimeter: s = 16.5

Angle ∠ A = α = 29.99547255274° = 29°59'41″ = 0.52435067187 rad
Angle ∠ B = β = 58.98220811689° = 58°58'55″ = 1.02994315161 rad
Angle ∠ C = γ = 91.02331933037° = 91°1'23″ = 1.58986544188 rad

Height: ha = 11.99880865821
Height: hb = 6.99988838396
Height: hc = 5.99990432911

Median: ma = 12.56598566871
Median: mb = 9.30105376189
Median: mc = 6.8922024376

Inradius: r = 2.54550486689
Circumradius: R = 7.00111163384

Vertex coordinates: A[14; 0] B[0; 0] C[3.60771428571; 5.99990432911]
Centroid: CG[5.8699047619; 21.999681097]
Coordinates of the circumscribed circle: U[7; -0.12550199346]
Coordinates of the inscribed circle: I[4.5; 2.54550486689]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.0055274473° = 150°19″ = 0.52435067187 rad
∠ B' = β' = 121.0187918831° = 121°1'5″ = 1.02994315161 rad
∠ C' = γ' = 88.97768066963° = 88°58'37″ = 1.58986544188 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 = 12 ; ; c = 14 ; ;

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

p = a+b+c = 7+12+14 = 33 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 33 }{ 2 } = 16.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16.5 * (16.5-7)(16.5-12)(16.5-14) } ; ; T = sqrt{ 1763.44 } = 41.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 41.99 }{ 7 } = 12 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 41.99 }{ 12 } = 7 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 41.99 }{ 14 } = 6 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 12**2+14**2-7**2 }{ 2 * 12 * 14 } ) = 29° 59'41" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 7**2+14**2-12**2 }{ 2 * 7 * 14 } ) = 58° 58'55" ; ; gamma = 180° - alpha - beta = 180° - 29° 59'41" - 58° 58'55" = 91° 1'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 41.99 }{ 16.5 } = 2.55 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 7 }{ 2 * sin 29° 59'41" } = 7 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 12**2+2 * 14**2 - 7**2 } }{ 2 } = 12.56 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 14**2+2 * 7**2 - 12**2 } }{ 2 } = 9.301 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 12**2+2 * 7**2 - 14**2 } }{ 2 } = 6.892 ; ;
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