4 27 30 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 27   c = 30

Area: T = 37.60990082294
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 5.32882629454° = 5°19'42″ = 0.09329957318 rad
Angle ∠ B = β = 38.81656606129° = 38°48'56″ = 0.6777461079 rad
Angle ∠ C = γ = 135.8566076442° = 135°51'22″ = 2.37111358427 rad

Height: ha = 18.80545041147
Height: hb = 2.78658524614
Height: hc = 2.50772672153

Median: ma = 28.4699281691
Median: mb = 16.60657219054
Median: mc = 12.14549578015

Inradius: r = 1.2333082237
Circumradius: R = 21.53773932505

Vertex coordinates: A[30; 0] B[0; 0] C[3.11766666667; 2.50772672153]
Centroid: CG[11.03988888889; 0.83657557384]
Coordinates of the circumscribed circle: U[15; -15.45550738603]
Coordinates of the inscribed circle: I[3.5; 1.2333082237]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 174.6721737055° = 174°40'18″ = 0.09329957318 rad
∠ B' = β' = 141.1844339387° = 141°11'4″ = 0.6777461079 rad
∠ C' = γ' = 44.14439235583° = 44°8'38″ = 2.37111358427 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 = 4 ; ; b = 27 ; ; c = 30 ; ;

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

p = a+b+c = 4+27+30 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-4)(30.5-27)(30.5-30) } ; ; T = sqrt{ 1414.44 } = 37.61 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 37.61 }{ 4 } = 18.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 37.61 }{ 27 } = 2.79 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 37.61 }{ 30 } = 2.51 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 27**2+30**2-4**2 }{ 2 * 27 * 30 } ) = 5° 19'42" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 4**2+30**2-27**2 }{ 2 * 4 * 30 } ) = 38° 48'56" ; ; gamma = 180° - alpha - beta = 180° - 5° 19'42" - 38° 48'56" = 135° 51'22" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 37.61 }{ 30.5 } = 1.23 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 4 }{ 2 * sin 5° 19'42" } = 21.54 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 27**2+2 * 30**2 - 4**2 } }{ 2 } = 28.469 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 30**2+2 * 4**2 - 27**2 } }{ 2 } = 16.606 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 27**2+2 * 4**2 - 30**2 } }{ 2 } = 12.145 ; ;
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