18 21 30 triangle

Obtuse scalene triangle.

Sides: a = 18   b = 21   c = 30

Area: T = 185.9622193738
Perimeter: p = 69
Semiperimeter: s = 34.5

Angle ∠ A = α = 36.18222872212° = 36°10'56″ = 0.63215000429 rad
Angle ∠ B = β = 43.53111521674° = 43°31'52″ = 0.76597619325 rad
Angle ∠ C = γ = 100.2876560611° = 100°17'12″ = 1.75503306782 rad

Height: ha = 20.66224659709
Height: hb = 17.71106851179
Height: hc = 12.39774795826

Median: ma = 24.28796210844
Median: mb = 22.43997767846
Median: mc = 12.5549900398

Inradius: r = 5.39902085142
Circumradius: R = 15.24550341815

Vertex coordinates: A[30; 0] B[0; 0] C[13.05; 12.39774795826]
Centroid: CG[14.35; 4.13224931942]
Coordinates of the circumscribed circle: U[15; -2.72223275324]
Coordinates of the inscribed circle: I[13.5; 5.39902085142]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.8187712779° = 143°49'4″ = 0.63215000429 rad
∠ B' = β' = 136.4698847833° = 136°28'8″ = 0.76597619325 rad
∠ C' = γ' = 79.71334393885° = 79°42'48″ = 1.75503306782 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 = 21 ; ; c = 30 ; ;

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

p = a+b+c = 18+21+30 = 69 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 69 }{ 2 } = 34.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34.5 * (34.5-18)(34.5-21)(34.5-30) } ; ; T = sqrt{ 34581.94 } = 185.96 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 185.96 }{ 18 } = 20.66 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 185.96 }{ 21 } = 17.71 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 185.96 }{ 30 } = 12.4 ; ;

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**2-21**2-30**2 }{ 2 * 21 * 30 } ) = 36° 10'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-18**2-30**2 }{ 2 * 18 * 30 } ) = 43° 31'52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-18**2-21**2 }{ 2 * 21 * 18 } ) = 100° 17'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 185.96 }{ 34.5 } = 5.39 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 36° 10'56" } = 15.25 ; ;




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