153 90 179.91 triangle

Obtuse scalene triangle.

Sides: a = 153   b = 90   c = 179.91

Area: T = 6881.653310868
Perimeter: p = 422.91
Semiperimeter: s = 211.455

Angle ∠ A = α = 58.21329538663° = 58°12'47″ = 1.01660077123 rad
Angle ∠ B = β = 300.0004595932° = 30°2″ = 0.5243606797 rad
Angle ∠ C = γ = 91.78765865405° = 91°47'12″ = 1.60219781443 rad

Height: ha = 89.95662497866
Height: hb = 152.9265624637
Height: hc = 76.50110628501

Median: ma = 119.9233117246
Median: mb = 160.8210720214
Median: mc = 87.5366266627

Inradius: r = 32.54442912614
Circumradius: R = 89.99987496055

Vertex coordinates: A[179.91; 0] B[0; 0] C[132.5011273137; 76.50110628501]
Centroid: CG[104.1377091046; 25.55003542834]
Coordinates of the circumscribed circle: U[89.955; -2.80658698403]
Coordinates of the inscribed circle: I[121.455; 32.54442912614]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 121.7877046134° = 121°47'13″ = 1.01660077123 rad
∠ B' = β' = 1509.999540407° = 149°59'58″ = 0.5243606797 rad
∠ C' = γ' = 88.21334134595° = 88°12'48″ = 1.60219781443 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 = 153 ; ; b = 90 ; ; c = 179.91 ; ;

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

p = a+b+c = 153+90+179.91 = 422.91 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 422.91 }{ 2 } = 211.46 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 211.46 * (211.46-153)(211.46-90)(211.46-179.91) } ; ; T = sqrt{ 47357149.51 } = 6881.65 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6881.65 }{ 153 } = 89.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6881.65 }{ 90 } = 152.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6881.65 }{ 179.91 } = 76.5 ; ;

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{ 90**2+179.91**2-153**2 }{ 2 * 90 * 179.91 } ) = 58° 12'47" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 153**2+179.91**2-90**2 }{ 2 * 153 * 179.91 } ) = 30° 2" ; ; gamma = 180° - alpha - beta = 180° - 58° 12'47" - 30° 2" = 91° 47'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6881.65 }{ 211.46 } = 32.54 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 153 }{ 2 * sin 58° 12'47" } = 90 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 179.91**2 - 153**2 } }{ 2 } = 119.923 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 179.91**2+2 * 153**2 - 90**2 } }{ 2 } = 160.821 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 153**2 - 179.91**2 } }{ 2 } = 87.536 ; ;
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