18 26 30 triangle

Acute scalene triangle.

Sides: a = 18   b = 26   c = 30

Area: T = 232.6610697154
Perimeter: p = 74
Semiperimeter: s = 37

Angle ∠ A = α = 36.62443415398° = 36°37'28″ = 0.63992153462 rad
Angle ∠ B = β = 59.50987077655° = 59°30'31″ = 1.03986228841 rad
Angle ∠ C = γ = 83.86769506947° = 83°52'1″ = 1.46437544232 rad

Height: ha = 25.85111885726
Height: hb = 17.89769767041
Height: hc = 15.51107131436

Median: ma = 26.58994716006
Median: mb = 21.04875651798
Median: mc = 16.58331239518

Inradius: r = 6.28881269501
Circumradius: R = 15.08663469548

Vertex coordinates: A[30; 0] B[0; 0] C[9.13333333333; 15.51107131436]
Centroid: CG[13.04444444444; 5.17702377145]
Coordinates of the circumscribed circle: U[15; 1.61217892046]
Coordinates of the inscribed circle: I[11; 6.28881269501]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.376565846° = 143°22'32″ = 0.63992153462 rad
∠ B' = β' = 120.4911292234° = 120°29'29″ = 1.03986228841 rad
∠ C' = γ' = 96.13330493053° = 96°7'59″ = 1.46437544232 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 = 18 ; ; b = 26 ; ; c = 30 ; ;

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

p = a+b+c = 18+26+30 = 74 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 74 }{ 2 } = 37 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37 * (37-18)(37-26)(37-30) } ; ; T = sqrt{ 54131 } = 232.66 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 232.66 }{ 18 } = 25.85 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 232.66 }{ 26 } = 17.9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 232.66 }{ 30 } = 15.51 ; ;

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{ 18**2-26**2-30**2 }{ 2 * 26 * 30 } ) = 36° 37'28" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-18**2-30**2 }{ 2 * 18 * 30 } ) = 59° 30'31" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-18**2-26**2 }{ 2 * 26 * 18 } ) = 83° 52'1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 232.66 }{ 37 } = 6.29 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 36° 37'28" } = 15.09 ; ;




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