12 23 26 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 23   c = 26

Area: T = 137.9987961941
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 27.48659860152° = 27°29'10″ = 0.48797209541 rad
Angle ∠ B = β = 62.20326223458° = 62°12'9″ = 1.08656405633 rad
Angle ∠ C = γ = 90.3111391639° = 90°18'41″ = 1.57662311362 rad

Height: ha = 232.9996603236
Height: hb = 121.9998227775
Height: hc = 10.61552278417

Median: ma = 23.80112604708
Median: mb = 16.66658333125
Median: mc = 12.94221791055

Inradius: r = 4.52545233423
Circumradius: R = 133.0001919939

Vertex coordinates: A[26; 0] B[0; 0] C[5.59661538462; 10.61552278417]
Centroid: CG[10.53220512821; 3.53884092806]
Coordinates of the circumscribed circle: U[13; -0.07106532174]
Coordinates of the inscribed circle: I[7.5; 4.52545233423]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.5144013985° = 152°30'50″ = 0.48797209541 rad
∠ B' = β' = 117.7977377654° = 117°47'51″ = 1.08656405633 rad
∠ C' = γ' = 89.6898608361° = 89°41'19″ = 1.57662311362 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 = 12 ; ; b = 23 ; ; c = 26 ; ;

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

p = a+b+c = 12+23+26 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-12)(30.5-23)(30.5-26) } ; ; T = sqrt{ 19043.44 } = 138 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 138 }{ 12 } = 23 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 138 }{ 23 } = 12 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 138 }{ 26 } = 10.62 ; ;

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{ 12**2-23**2-26**2 }{ 2 * 23 * 26 } ) = 27° 29'10" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-12**2-26**2 }{ 2 * 12 * 26 } ) = 62° 12'9" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-12**2-23**2 }{ 2 * 23 * 12 } ) = 90° 18'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 138 }{ 30.5 } = 4.52 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 27° 29'10" } = 13 ; ;




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