18 29 30 triangle

Acute scalene triangle.

Sides: a = 18   b = 29   c = 30

Area: T = 252.4521851845
Perimeter: p = 77
Semiperimeter: s = 38.5

Angle ∠ A = α = 35.47550991434° = 35°28'30″ = 0.61991572825 rad
Angle ∠ B = β = 69.22992530508° = 69°13'45″ = 1.20882784044 rad
Angle ∠ C = γ = 75.29656478059° = 75°17'44″ = 1.31441569666 rad

Height: ha = 28.05502057606
Height: hb = 17.4110472541
Height: hc = 16.83301234563

Median: ma = 28.09880426365
Median: mb = 20.04437022528
Median: mc = 18.90876704012

Inradius: r = 6.5577190957
Circumradius: R = 15.50879076322

Vertex coordinates: A[30; 0] B[0; 0] C[6.38333333333; 16.83301234563]
Centroid: CG[12.12877777778; 5.61100411521]
Coordinates of the circumscribed circle: U[15; 3.93663941787]
Coordinates of the inscribed circle: I[9.5; 6.5577190957]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.5254900857° = 144°31'30″ = 0.61991572825 rad
∠ B' = β' = 110.7710746949° = 110°46'15″ = 1.20882784044 rad
∠ C' = γ' = 104.7044352194° = 104°42'16″ = 1.31441569666 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 = 29 ; ; c = 30 ; ;

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

p = a+b+c = 18+29+30 = 77 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 77 }{ 2 } = 38.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 38.5 * (38.5-18)(38.5-29)(38.5-30) } ; ; T = sqrt{ 63731.94 } = 252.45 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 252.45 }{ 18 } = 28.05 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 252.45 }{ 29 } = 17.41 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 252.45 }{ 30 } = 16.83 ; ;

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**2-29**2-30**2 }{ 2 * 29 * 30 } ) = 35° 28'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-18**2-30**2 }{ 2 * 18 * 30 } ) = 69° 13'45" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-18**2-29**2 }{ 2 * 29 * 18 } ) = 75° 17'44" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 252.45 }{ 38.5 } = 6.56 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 35° 28'30" } = 15.51 ; ;




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