7 11 16 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 11   c = 16

Area: T = 31.93774388453
Perimeter: p = 34
Semiperimeter: s = 17

Angle ∠ A = α = 21.28799664684° = 21°16'48″ = 0.37114054796 rad
Angle ∠ B = β = 34.77219440319° = 34°46'19″ = 0.60768849107 rad
Angle ∠ C = γ = 123.94880895° = 123°56'53″ = 2.16333022633 rad

Height: ha = 9.12549825272
Height: hb = 5.80768070628
Height: hc = 3.99221798557

Median: ma = 13.27659180474
Median: mb = 11.05766721937
Median: mc = 4.5832575695

Inradius: r = 1.87986728733
Circumradius: R = 9.64438540827

Vertex coordinates: A[16; 0] B[0; 0] C[5.75; 3.99221798557]
Centroid: CG[7.25; 1.33107266186]
Coordinates of the circumscribed circle: U[8; -5.38655289033]
Coordinates of the inscribed circle: I[6; 1.87986728733]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.7220033532° = 158°43'12″ = 0.37114054796 rad
∠ B' = β' = 145.2288055968° = 145°13'41″ = 0.60768849107 rad
∠ C' = γ' = 56.05219105004° = 56°3'7″ = 2.16333022633 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 = 16 ; ;

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

p = a+b+c = 7+11+16 = 34 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 34 }{ 2 } = 17 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17 * (17-7)(17-11)(17-16) } ; ; T = sqrt{ 1020 } = 31.94 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 31.94 }{ 7 } = 9.12 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 31.94 }{ 11 } = 5.81 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 31.94 }{ 16 } = 3.99 ; ;

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**2-16**2 }{ 2 * 11 * 16 } ) = 21° 16'48" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-7**2-16**2 }{ 2 * 7 * 16 } ) = 34° 46'19" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-7**2-11**2 }{ 2 * 11 * 7 } ) = 123° 56'53" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 31.94 }{ 17 } = 1.88 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 21° 16'48" } = 9.64 ; ;




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