8 11 14 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 11   c = 14

Area: T = 43.91439784123
Perimeter: p = 33
Semiperimeter: s = 16.5

Angle ∠ A = α = 34.77219440319° = 34°46'19″ = 0.60768849107 rad
Angle ∠ B = β = 51.64547342696° = 51°38'41″ = 0.90113706543 rad
Angle ∠ C = γ = 93.58333216985° = 93°35' = 1.63333370886 rad

Height: ha = 10.97884946031
Height: hb = 7.98443597113
Height: hc = 6.27334254875

Median: ma = 11.93773363863
Median: mb = 9.98774921777
Median: mc = 6.59554529791

Inradius: r = 2.66114532371
Circumradius: R = 7.01437120602

Vertex coordinates: A[14; 0] B[0; 0] C[4.96442857143; 6.27334254875]
Centroid: CG[6.32114285714; 2.09111418292]
Coordinates of the circumscribed circle: U[7; -0.43883570038]
Coordinates of the inscribed circle: I[5.5; 2.66114532371]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.2288055968° = 145°13'41″ = 0.60768849107 rad
∠ B' = β' = 128.355526573° = 128°21'19″ = 0.90113706543 rad
∠ C' = γ' = 86.41766783015° = 86°25' = 1.63333370886 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 = 8 ; ; b = 11 ; ; c = 14 ; ;

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

p = a+b+c = 8+11+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 * (16.5-8)(16.5-11)(16.5-14) } ; ; T = sqrt{ 1928.44 } = 43.91 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 43.91 }{ 8 } = 10.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 43.91 }{ 11 } = 7.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 43.91 }{ 14 } = 6.27 ; ;

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{ 8**2-11**2-14**2 }{ 2 * 11 * 14 } ) = 34° 46'19" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-8**2-14**2 }{ 2 * 8 * 14 } ) = 51° 38'41" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14**2-8**2-11**2 }{ 2 * 11 * 8 } ) = 93° 35' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 43.91 }{ 16.5 } = 2.66 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 34° 46'19" } = 7.01 ; ;




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