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

Calculate another triangle




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 ; ;
Calculate another triangle

Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.