18 20 30 triangle

Obtuse scalene triangle.

Sides: a = 18   b = 20   c = 30

Area: T = 174.5399393834
Perimeter: p = 68
Semiperimeter: s = 34

Angle ∠ A = α = 35.57771025511° = 35°34'38″ = 0.62109375778 rad
Angle ∠ B = β = 40.274389294° = 40°16'26″ = 0.70329120344 rad
Angle ∠ C = γ = 104.1499004509° = 104°8'56″ = 1.81877430414 rad

Height: ha = 19.39332659816
Height: hb = 17.45439393834
Height: hc = 11.63659595889

Median: ma = 23.85437208838
Median: mb = 22.6277416998
Median: mc = 11.70546999107

Inradius: r = 5.13435115834
Circumradius: R = 15.46992871374

Vertex coordinates: A[30; 0] B[0; 0] C[13.73333333333; 11.63659595889]
Centroid: CG[14.57877777778; 3.87986531963]
Coordinates of the circumscribed circle: U[15; -3.78113813002]
Coordinates of the inscribed circle: I[14; 5.13435115834]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.4232897449° = 144°25'22″ = 0.62109375778 rad
∠ B' = β' = 139.726610706° = 139°43'34″ = 0.70329120344 rad
∠ C' = γ' = 75.85109954911° = 75°51'4″ = 1.81877430414 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 = 20 ; ; c = 30 ; ;

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

p = a+b+c = 18+20+30 = 68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 68 }{ 2 } = 34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34 * (34-18)(34-20)(34-30) } ; ; T = sqrt{ 30464 } = 174.54 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 174.54 }{ 18 } = 19.39 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 174.54 }{ 20 } = 17.45 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 174.54 }{ 30 } = 11.64 ; ;

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**2-20**2-30**2 }{ 2 * 20 * 30 } ) = 35° 34'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-18**2-30**2 }{ 2 * 18 * 30 } ) = 40° 16'26" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-18**2-20**2 }{ 2 * 20 * 18 } ) = 104° 8'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 174.54 }{ 34 } = 5.13 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 35° 34'38" } = 15.47 ; ;




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