8.3 8.1 0.75 triangle

Obtuse scalene triangle.

Sides: a = 8.3   b = 8.1   c = 0.75

Area: T = 2.96105499252
Perimeter: p = 17.15
Semiperimeter: s = 8.575

Angle ∠ A = α = 102.9244243841° = 102°55'27″ = 1.79663669351 rad
Angle ∠ B = β = 72.02330393212° = 72°1'23″ = 1.25770391734 rad
Angle ∠ C = γ = 5.0532716838° = 5°3'10″ = 0.0888186545 rad

Height: ha = 0.71333855241
Height: hb = 0.73109999815
Height: hc = 7.89547998004

Median: ma = 3.98329323369
Median: mb = 4.28106249544
Median: mc = 8.19220311889

Inradius: r = 0.34552536356
Circumradius: R = 4.25878660447

Vertex coordinates: A[0.75; 0] B[0; 0] C[2.56216666667; 7.89547998004]
Centroid: CG[1.10438888889; 2.63215999335]
Coordinates of the circumscribed circle: U[0.375; 4.24113203433]
Coordinates of the inscribed circle: I[0.475; 0.34552536356]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 77.07657561592° = 77°4'33″ = 1.79663669351 rad
∠ B' = β' = 107.9776960679° = 107°58'37″ = 1.25770391734 rad
∠ C' = γ' = 174.9477283162° = 174°56'50″ = 0.0888186545 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 = 8.3 ; ; b = 8.1 ; ; c = 0.75 ; ;

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

p = a+b+c = 8.3+8.1+0.75 = 17.15 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 17.15 }{ 2 } = 8.58 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.58 * (8.58-8.3)(8.58-8.1)(8.58-0.75) } ; ; T = sqrt{ 8.76 } = 2.96 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2.96 }{ 8.3 } = 0.71 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2.96 }{ 8.1 } = 0.73 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2.96 }{ 0.75 } = 7.89 ; ;

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{ 8.1**2+0.75**2-8.3**2 }{ 2 * 8.1 * 0.75 } ) = 102° 55'27" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 8.3**2+0.75**2-8.1**2 }{ 2 * 8.3 * 0.75 } ) = 72° 1'23" ; ;
 gamma = 180° - alpha - beta = 180° - 102° 55'27" - 72° 1'23" = 5° 3'10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2.96 }{ 8.58 } = 0.35 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 8.3 }{ 2 * sin 102° 55'27" } = 4.26 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.1**2+2 * 0.75**2 - 8.3**2 } }{ 2 } = 3.983 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.75**2+2 * 8.3**2 - 8.1**2 } }{ 2 } = 4.281 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.1**2+2 * 8.3**2 - 0.75**2 } }{ 2 } = 8.192 ; ;
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