8.14 33 33.99 triangle

Obtuse scalene triangle.

Sides: a = 8.14   b = 33   c = 33.99

Area: T = 134.3109999148
Perimeter: p = 75.13
Semiperimeter: s = 37.565

Angle ∠ A = α = 13.85659813612° = 13°51'22″ = 0.24218324958 rad
Angle ∠ B = β = 76.13875664114° = 76°8'15″ = 1.32988512183 rad
Angle ∠ C = γ = 90.00664522274° = 90°23″ = 1.57109089394 rad

Height: ha = 332.9999997908
Height: hb = 8.14399999484
Height: hc = 7.90329125712

Median: ma = 33.25504909738
Median: mb = 18.39994524375
Median: mc = 16.99441100091

Inradius: r = 3.57554026128
Circumradius: R = 16.99550001078

Vertex coordinates: A[33.99; 0] B[0; 0] C[1.95502750809; 7.90329125712]
Centroid: CG[11.98800916936; 2.63443041904]
Coordinates of the circumscribed circle: U[16.995; -0.00219138514]
Coordinates of the inscribed circle: I[4.565; 3.57554026128]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.1444018639° = 166°8'38″ = 0.24218324958 rad
∠ B' = β' = 103.8622433589° = 103°51'45″ = 1.32988512183 rad
∠ C' = γ' = 89.99435477726° = 89°59'37″ = 1.57109089394 rad

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How did we calculate this triangle?

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

p = a+b+c = 8.14+33+33.99 = 75.13 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 75.13 }{ 2 } = 37.57 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37.57 * (37.57-8.14)(37.57-33)(37.57-33.99) } ; ; T = sqrt{ 18039.18 } = 134.31 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 134.31 }{ 8.14 } = 33 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 134.31 }{ 33 } = 8.14 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 134.31 }{ 33.99 } = 7.9 ; ;

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{ 33**2+33.99**2-8.14**2 }{ 2 * 33 * 33.99 } ) = 13° 51'22" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 8.14**2+33.99**2-33**2 }{ 2 * 8.14 * 33.99 } ) = 76° 8'15" ; ;
 gamma = 180° - alpha - beta = 180° - 13° 51'22" - 76° 8'15" = 90° 23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 134.31 }{ 37.57 } = 3.58 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 8.14 }{ 2 * sin 13° 51'22" } = 17 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 33**2+2 * 33.99**2 - 8.14**2 } }{ 2 } = 33.25 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 33.99**2+2 * 8.14**2 - 33**2 } }{ 2 } = 18.399 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 33**2+2 * 8.14**2 - 33.99**2 } }{ 2 } = 16.994 ; ;
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