7 20 23 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 20   c = 23

Area: T = 67.0822039325
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 16.95774262942° = 16°57'27″ = 0.29659629215 rad
Angle ∠ B = β = 56.44110241068° = 56°26'28″ = 0.98550817039 rad
Angle ∠ C = γ = 106.6021549599° = 106°36'6″ = 1.86105480282 rad

Height: ha = 19.166629695
Height: hb = 6.70882039325
Height: hc = 5.83332208109

Median: ma = 21.26661703181
Median: mb = 13.74877270849
Median: mc = 9.60546863561

Inradius: r = 2.6833281573
Circumradius: R = 122.0002314792

Vertex coordinates: A[23; 0] B[0; 0] C[3.87695652174; 5.83332208109]
Centroid: CG[8.95765217391; 1.9444406937]
Coordinates of the circumscribed circle: U[11.5; -3.42986375655]
Coordinates of the inscribed circle: I[5; 2.6833281573]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.0432573706° = 163°2'33″ = 0.29659629215 rad
∠ B' = β' = 123.5598975893° = 123°33'32″ = 0.98550817039 rad
∠ C' = γ' = 73.3988450401° = 73°23'54″ = 1.86105480282 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 = 7 ; ; b = 20 ; ; c = 23 ; ;

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

p = a+b+c = 7+20+23 = 50 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 50 }{ 2 } = 25 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25 * (25-7)(25-20)(25-23) } ; ; T = sqrt{ 4500 } = 67.08 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 67.08 }{ 7 } = 19.17 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 67.08 }{ 20 } = 6.71 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 67.08 }{ 23 } = 5.83 ; ;

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{ 7**2-20**2-23**2 }{ 2 * 20 * 23 } ) = 16° 57'27" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-7**2-23**2 }{ 2 * 7 * 23 } ) = 56° 26'28" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-7**2-20**2 }{ 2 * 20 * 7 } ) = 106° 36'6" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 67.08 }{ 25 } = 2.68 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 16° 57'27" } = 12 ; ;




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