177 124 63 triangle

Obtuse scalene triangle.

Sides: a = 177   b = 124   c = 63

Area: T = 2506.15664197
Perimeter: p = 364
Semiperimeter: s = 182

Angle ∠ A = α = 140.0877490949° = 140°5'15″ = 2.44549879579 rad
Angle ∠ B = β = 26.71112543219° = 26°42'40″ = 0.46661993353 rad
Angle ∠ C = γ = 13.20112547288° = 13°12'5″ = 0.23304053604 rad

Height: ha = 28.3188151635
Height: hb = 40.42218777371
Height: hc = 79.56105212603

Median: ma = 42.89881351576
Median: mb = 117.4954680731
Median: mc = 149.5333441076

Inradius: r = 13.77700902181
Circumradius: R = 137.9332731286

Vertex coordinates: A[63; 0] B[0; 0] C[158.1111111111; 79.56105212603]
Centroid: CG[73.70437037037; 26.52201737534]
Coordinates of the circumscribed circle: U[31.5; 134.2887707405]
Coordinates of the inscribed circle: I[58; 13.77700902181]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 39.91325090507° = 39°54'45″ = 2.44549879579 rad
∠ B' = β' = 153.2898745678° = 153°17'20″ = 0.46661993353 rad
∠ C' = γ' = 166.7998745271° = 166°47'56″ = 0.23304053604 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 = 177 ; ; b = 124 ; ; c = 63 ; ;

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

p = a+b+c = 177+124+63 = 364 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 364 }{ 2 } = 182 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 182 * (182-177)(182-124)(182-63) } ; ; T = sqrt{ 6280820 } = 2506.16 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2506.16 }{ 177 } = 28.32 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2506.16 }{ 124 } = 40.42 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2506.16 }{ 63 } = 79.56 ; ;

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{ 177**2-124**2-63**2 }{ 2 * 124 * 63 } ) = 140° 5'15" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 124**2-177**2-63**2 }{ 2 * 177 * 63 } ) = 26° 42'40" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 63**2-177**2-124**2 }{ 2 * 124 * 177 } ) = 13° 12'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2506.16 }{ 182 } = 13.77 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 177 }{ 2 * sin 140° 5'15" } = 137.93 ; ;




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