232 100 171.3 triangle

Obtuse scalene triangle.

Sides: a = 232   b = 100   c = 171.3

Area: T = 7762.362200483
Perimeter: p = 503.3
Semiperimeter: s = 251.65

Angle ∠ A = α = 115.0032598816° = 115°9″ = 2.00771739977 rad
Angle ∠ B = β = 22.99444303335° = 22°59'40″ = 0.40113285189 rad
Angle ∠ C = γ = 42.00329708501° = 42°11″ = 0.7333090137 rad

Height: ha = 66.91769138347
Height: hb = 155.2477240097
Height: hc = 90.62988617026

Median: ma = 78.84106303881
Median: mb = 197.6966345439
Median: mc = 156.7687590719

Inradius: r = 30.84658653083
Circumradius: R = 127.995454591

Vertex coordinates: A[171.3; 0] B[0; 0] C[213.5665936953; 90.62988617026]
Centroid: CG[128.2898645651; 30.21096205675]
Coordinates of the circumscribed circle: U[85.65; 95.11440435625]
Coordinates of the inscribed circle: I[151.65; 30.84658653083]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 64.99774011836° = 64°59'51″ = 2.00771739977 rad
∠ B' = β' = 157.0065569666° = 157°20″ = 0.40113285189 rad
∠ C' = γ' = 137.997702915° = 137°59'49″ = 0.7333090137 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 = 232 ; ; b = 100 ; ; c = 171.3 ; ;

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

p = a+b+c = 232+100+171.3 = 503.3 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 503.3 }{ 2 } = 251.65 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 251.65 * (251.65-232)(251.65-100)(251.65-171.3) } ; ; T = sqrt{ 60254263.89 } = 7762.36 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 7762.36 }{ 232 } = 66.92 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 7762.36 }{ 100 } = 155.25 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 7762.36 }{ 171.3 } = 90.63 ; ;

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{ 100**2+171.3**2-232**2 }{ 2 * 100 * 171.3 } ) = 115° 9" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 232**2+171.3**2-100**2 }{ 2 * 232 * 171.3 } ) = 22° 59'40" ; ;
 gamma = 180° - alpha - beta = 180° - 115° 9" - 22° 59'40" = 42° 11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 7762.36 }{ 251.65 } = 30.85 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 232 }{ 2 * sin 115° 9" } = 127.99 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 100**2+2 * 171.3**2 - 232**2 } }{ 2 } = 78.841 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 171.3**2+2 * 232**2 - 100**2 } }{ 2 } = 197.696 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 100**2+2 * 232**2 - 171.3**2 } }{ 2 } = 156.768 ; ;
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