18 22 30 triangle

Obtuse scalene triangle.

Sides: a = 18   b = 22   c = 30

Area: T = 196.6659604393
Perimeter: p = 70
Semiperimeter: s = 35

Angle ∠ A = α = 36.58795428375° = 36°34'46″ = 0.63884334614 rad
Angle ∠ B = β = 46.75498273458° = 46°44'59″ = 0.81659384119 rad
Angle ∠ C = γ = 96.67106298167° = 96°40'14″ = 1.68772207803 rad

Height: ha = 21.85110671548
Height: hb = 17.87881458539
Height: hc = 13.11106402929

Median: ma = 24.71884141886
Median: mb = 22.15985198062
Median: mc = 13.37990881603

Inradius: r = 5.61988458398
Circumradius: R = 15.10222372346

Vertex coordinates: A[30; 0] B[0; 0] C[12.33333333333; 13.11106402929]
Centroid: CG[14.11111111111; 4.3770213431]
Coordinates of the circumscribed circle: U[15; -1.75443002848]
Coordinates of the inscribed circle: I[13; 5.61988458398]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.4220457162° = 143°25'14″ = 0.63884334614 rad
∠ B' = β' = 133.2550172654° = 133°15'1″ = 0.81659384119 rad
∠ C' = γ' = 83.32993701833° = 83°19'46″ = 1.68772207803 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 = 22 ; ; c = 30 ; ;

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

p = a+b+c = 18+22+30 = 70 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 70 }{ 2 } = 35 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35 * (35-18)(35-22)(35-30) } ; ; T = sqrt{ 38675 } = 196.66 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 196.66 }{ 18 } = 21.85 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 196.66 }{ 22 } = 17.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 196.66 }{ 30 } = 13.11 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 22**2+30**2-18**2 }{ 2 * 22 * 30 } ) = 36° 34'46" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 18**2+30**2-22**2 }{ 2 * 18 * 30 } ) = 46° 44'59" ; ; gamma = 180° - alpha - beta = 180° - 36° 34'46" - 46° 44'59" = 96° 40'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 196.66 }{ 35 } = 5.62 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 18 }{ 2 * sin 36° 34'46" } = 15.1 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 22**2+2 * 30**2 - 18**2 } }{ 2 } = 24.718 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 30**2+2 * 18**2 - 22**2 } }{ 2 } = 22.159 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 22**2+2 * 18**2 - 30**2 } }{ 2 } = 13.379 ; ;
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