10 23 30 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 23   c = 30

Area: T = 92.92443644046
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 15.62553527918° = 15°37'31″ = 0.2732713853 rad
Angle ∠ B = β = 38.27993217379° = 38°16'46″ = 0.66881001998 rad
Angle ∠ C = γ = 126.095532547° = 126°5'43″ = 2.20107786008 rad

Height: ha = 18.58548728809
Height: hb = 8.08803795134
Height: hc = 6.1954957627

Median: ma = 26.2588332011
Median: mb = 19.17768089108
Median: mc = 9.46604439642

Inradius: r = 2.95499798224
Circumradius: R = 18.56334845183

Vertex coordinates: A[30; 0] B[0; 0] C[7.85; 6.1954957627]
Centroid: CG[12.61766666667; 2.06549858757]
Coordinates of the circumscribed circle: U[15; -10.93663137054]
Coordinates of the inscribed circle: I[8.5; 2.95499798224]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.3754647208° = 164°22'29″ = 0.2732713853 rad
∠ B' = β' = 141.7210678262° = 141°43'14″ = 0.66881001998 rad
∠ C' = γ' = 53.90546745297° = 53°54'17″ = 2.20107786008 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 = 10 ; ; b = 23 ; ; c = 30 ; ;

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

p = a+b+c = 10+23+30 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-10)(31.5-23)(31.5-30) } ; ; T = sqrt{ 8634.94 } = 92.92 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 92.92 }{ 10 } = 18.58 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 92.92 }{ 23 } = 8.08 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 92.92 }{ 30 } = 6.19 ; ;

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{ 10**2-23**2-30**2 }{ 2 * 23 * 30 } ) = 15° 37'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-10**2-30**2 }{ 2 * 10 * 30 } ) = 38° 16'46" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-10**2-23**2 }{ 2 * 23 * 10 } ) = 126° 5'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 92.92 }{ 31.5 } = 2.95 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 15° 37'31" } = 18.56 ; ;




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