7 11 14 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 11   c = 14

Area: T = 37.9477331922
Perimeter: p = 32
Semiperimeter: s = 16

Angle ∠ A = α = 29.52662652473° = 29°31'35″ = 0.51553305444 rad
Angle ∠ B = β = 50.75438670503° = 50°45'14″ = 0.88658220881 rad
Angle ∠ C = γ = 99.72198677024° = 99°43'12″ = 1.74404400211 rad

Height: ha = 10.84220948349
Height: hb = 6.98995148949
Height: hc = 5.42110474174

Median: ma = 12.09333866224
Median: mb = 9.60546863561
Median: mc = 6

Inradius: r = 2.37217082451
Circumradius: R = 7.10219485785

Vertex coordinates: A[14; 0] B[0; 0] C[4.42985714286; 5.42110474174]
Centroid: CG[6.14328571429; 1.80770158058]
Coordinates of the circumscribed circle: U[7; -1.19990302795]
Coordinates of the inscribed circle: I[5; 2.37217082451]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.4743734753° = 150°28'25″ = 0.51553305444 rad
∠ B' = β' = 129.246613295° = 129°14'46″ = 0.88658220881 rad
∠ C' = γ' = 80.28801322976° = 80°16'48″ = 1.74404400211 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 = 11 ; ; c = 14 ; ;

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

p = a+b+c = 7+11+14 = 32 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 32 }{ 2 } = 16 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16 * (16-7)(16-11)(16-14) } ; ; T = sqrt{ 1440 } = 37.95 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 37.95 }{ 7 } = 10.84 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 37.95 }{ 11 } = 6.9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 37.95 }{ 14 } = 5.42 ; ;

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**2-11**2-14**2 }{ 2 * 11 * 14 } ) = 29° 31'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-7**2-14**2 }{ 2 * 7 * 14 } ) = 50° 45'14" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14**2-7**2-11**2 }{ 2 * 11 * 7 } ) = 99° 43'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 37.95 }{ 16 } = 2.37 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 29° 31'35" } = 7.1 ; ;




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