7 23 28 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 23   c = 28

Area: T = 61.8710833193
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 11.07880164461° = 11°4'41″ = 0.19333478616 rad
Angle ∠ B = β = 39.14986876423° = 39°8'55″ = 0.68332734972 rad
Angle ∠ C = γ = 129.7733295912° = 129°46'24″ = 2.26549712948 rad

Height: ha = 17.67773809123
Height: hb = 5.38800724516
Height: hc = 4.41993452281

Median: ma = 25.3822080293
Median: mb = 16.86597153001
Median: mc = 9.6443650761

Inradius: r = 2.13334770067
Circumradius: R = 18.21553680796

Vertex coordinates: A[28; 0] B[0; 0] C[5.42985714286; 4.41993452281]
Centroid: CG[11.14328571429; 1.4733115076]
Coordinates of the circumscribed circle: U[14; -11.65333100136]
Coordinates of the inscribed circle: I[6; 2.13334770067]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.9221983554° = 168°55'19″ = 0.19333478616 rad
∠ B' = β' = 140.8511312358° = 140°51'5″ = 0.68332734972 rad
∠ C' = γ' = 50.22767040883° = 50°13'36″ = 2.26549712948 rad

Calculate another triangle




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 = 23 ; ; c = 28 ; ;

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

p = a+b+c = 7+23+28 = 58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 58 }{ 2 } = 29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29 * (29-7)(29-23)(29-28) } ; ; T = sqrt{ 3828 } = 61.87 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 61.87 }{ 7 } = 17.68 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 61.87 }{ 23 } = 5.38 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 61.87 }{ 28 } = 4.42 ; ;

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**2-23**2-28**2 }{ 2 * 23 * 28 } ) = 11° 4'41" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-7**2-28**2 }{ 2 * 7 * 28 } ) = 39° 8'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-7**2-23**2 }{ 2 * 23 * 7 } ) = 129° 46'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 61.87 }{ 29 } = 2.13 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 11° 4'41" } = 18.22 ; ;




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