23 26 30 triangle

Acute scalene triangle.

Sides: a = 23   b = 26   c = 30

Area: T = 289.1144056213
Perimeter: p = 79
Semiperimeter: s = 39.5

Angle ∠ A = α = 47.84438182214° = 47°50'38″ = 0.83550321547 rad
Angle ∠ B = β = 56.93107578126° = 56°55'51″ = 0.99436291695 rad
Angle ∠ C = γ = 75.2255423966° = 75°13'32″ = 1.31329313294 rad

Height: ha = 25.14403527142
Height: hb = 22.24395427856
Height: hc = 19.27442704142

Median: ma = 25.60876160546
Median: mb = 23.35659414283
Median: mc = 19.42993592277

Inradius: r = 7.31993431953
Circumradius: R = 15.51329088455

Vertex coordinates: A[30; 0] B[0; 0] C[12.55; 19.27442704142]
Centroid: CG[14.18333333333; 6.42547568047]
Coordinates of the circumscribed circle: U[15; 3.95660511688]
Coordinates of the inscribed circle: I[13.5; 7.31993431953]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.1566181779° = 132°9'22″ = 0.83550321547 rad
∠ B' = β' = 123.0699242187° = 123°4'9″ = 0.99436291695 rad
∠ C' = γ' = 104.7754576034° = 104°46'28″ = 1.31329313294 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 = 23 ; ; b = 26 ; ; c = 30 ; ;

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

p = a+b+c = 23+26+30 = 79 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 79 }{ 2 } = 39.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 39.5 * (39.5-23)(39.5-26)(39.5-30) } ; ; T = sqrt{ 83586.94 } = 289.11 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 289.11 }{ 23 } = 25.14 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 289.11 }{ 26 } = 22.24 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 289.11 }{ 30 } = 19.27 ; ;

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{ 23**2-26**2-30**2 }{ 2 * 26 * 30 } ) = 47° 50'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-23**2-30**2 }{ 2 * 23 * 30 } ) = 56° 55'51" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-23**2-26**2 }{ 2 * 26 * 23 } ) = 75° 13'32" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 289.11 }{ 39.5 } = 7.32 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 23 }{ 2 * sin 47° 50'38" } = 15.51 ; ;




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