18 19 30 triangle

Obtuse scalene triangle.

Sides: a = 18   b = 19   c = 30

Area: T = 162.3332798596
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 34.72215542035° = 34°43'18″ = 0.60660054423 rad
Angle ∠ B = β = 36.95882263138° = 36°57'30″ = 0.64550427349 rad
Angle ∠ C = γ = 108.3220219483° = 108°19'13″ = 1.89105444765 rad

Height: ha = 18.03769776218
Height: hb = 17.08876630101
Height: hc = 10.82221865731

Median: ma = 23.44114163395
Median: mb = 22.8421847561
Median: mc = 10.84397416943

Inradius: r = 4.8465755182
Circumradius: R = 15.80108734044

Vertex coordinates: A[30; 0] B[0; 0] C[14.38333333333; 10.82221865731]
Centroid: CG[14.79444444444; 3.60773955244]
Coordinates of the circumscribed circle: U[15; -4.9676648804]
Coordinates of the inscribed circle: I[14.5; 4.8465755182]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.2788445796° = 145°16'42″ = 0.60660054423 rad
∠ B' = β' = 143.0421773686° = 143°2'30″ = 0.64550427349 rad
∠ C' = γ' = 71.68797805173° = 71°40'47″ = 1.89105444765 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 = 18 ; ; b = 19 ; ; c = 30 ; ;

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

p = a+b+c = 18+19+30 = 67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67 }{ 2 } = 33.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.5 * (33.5-18)(33.5-19)(33.5-30) } ; ; T = sqrt{ 26351.94 } = 162.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 162.33 }{ 18 } = 18.04 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 162.33 }{ 19 } = 17.09 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 162.33 }{ 30 } = 10.82 ; ;

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**2-19**2-30**2 }{ 2 * 19 * 30 } ) = 34° 43'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-18**2-30**2 }{ 2 * 18 * 30 } ) = 36° 57'30" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-18**2-19**2 }{ 2 * 19 * 18 } ) = 108° 19'13" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 162.33 }{ 33.5 } = 4.85 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 34° 43'18" } = 15.8 ; ;




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

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