12 27 30 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 27   c = 30

Area: T = 161.8599313912
Perimeter: p = 69
Semiperimeter: s = 34.5

Angle ∠ A = α = 23.55664643091° = 23°33'23″ = 0.41111378623 rad
Angle ∠ B = β = 64.05655202276° = 64°3'20″ = 1.1187979732 rad
Angle ∠ C = γ = 92.38880154633° = 92°23'17″ = 1.61224750592 rad

Height: ha = 26.97765523186
Height: hb = 11.99895788083
Height: hc = 10.79106209275

Median: ma = 27.90216128566
Median: mb = 18.43223085912
Median: mc = 14.54330395722

Inradius: r = 4.69215743163
Circumradius: R = 15.01330378121

Vertex coordinates: A[30; 0] B[0; 0] C[5.25; 10.79106209275]
Centroid: CG[11.75; 3.59768736425]
Coordinates of the circumscribed circle: U[15; -0.62655432422]
Coordinates of the inscribed circle: I[7.5; 4.69215743163]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.4443535691° = 156°26'37″ = 0.41111378623 rad
∠ B' = β' = 115.9444479772° = 115°56'40″ = 1.1187979732 rad
∠ C' = γ' = 87.61219845367° = 87°36'43″ = 1.61224750592 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 = 12 ; ; b = 27 ; ; c = 30 ; ;

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

p = a+b+c = 12+27+30 = 69 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 69 }{ 2 } = 34.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34.5 * (34.5-12)(34.5-27)(34.5-30) } ; ; T = sqrt{ 26198.44 } = 161.86 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 161.86 }{ 12 } = 26.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 161.86 }{ 27 } = 11.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 161.86 }{ 30 } = 10.79 ; ;

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{ 12**2-27**2-30**2 }{ 2 * 27 * 30 } ) = 23° 33'23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-12**2-30**2 }{ 2 * 12 * 30 } ) = 64° 3'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-12**2-27**2 }{ 2 * 27 * 12 } ) = 92° 23'17" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 161.86 }{ 34.5 } = 4.69 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 23° 33'23" } = 15.01 ; ;




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

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