9 14 19 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 14   c = 19

Area: T = 59.39769696197
Perimeter: p = 42
Semiperimeter: s = 21

Angle ∠ A = α = 26.52553520166° = 26°31'31″ = 0.46329547279 rad
Angle ∠ B = β = 44.00334273489° = 44°12″ = 0.76880046894 rad
Angle ∠ C = γ = 109.4711220634° = 109°28'16″ = 1.91106332362 rad

Height: ha = 13.19993265821
Height: hb = 8.48552813742
Height: hc = 6.25223125915

Median: ma = 16.077015868
Median: mb = 13.11548770486
Median: mc = 6.94662219947

Inradius: r = 2.82884271247
Circumradius: R = 10.07662716319

Vertex coordinates: A[19; 0] B[0; 0] C[6.47436842105; 6.25223125915]
Centroid: CG[8.49112280702; 2.08441041972]
Coordinates of the circumscribed circle: U[9.5; -3.35987572106]
Coordinates of the inscribed circle: I[7; 2.82884271247]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.4754647983° = 153°28'29″ = 0.46329547279 rad
∠ B' = β' = 135.9976572651° = 135°59'48″ = 0.76880046894 rad
∠ C' = γ' = 70.52987793655° = 70°31'44″ = 1.91106332362 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 = 9 ; ; b = 14 ; ; c = 19 ; ;

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

p = a+b+c = 9+14+19 = 42 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 42 }{ 2 } = 21 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21 * (21-9)(21-14)(21-19) } ; ; T = sqrt{ 3528 } = 59.4 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 59.4 }{ 9 } = 13.2 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 59.4 }{ 14 } = 8.49 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 59.4 }{ 19 } = 6.25 ; ;

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{ 14**2+19**2-9**2 }{ 2 * 14 * 19 } ) = 26° 31'31" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 9**2+19**2-14**2 }{ 2 * 9 * 19 } ) = 44° 12" ; ; gamma = 180° - alpha - beta = 180° - 26° 31'31" - 44° 12" = 109° 28'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 59.4 }{ 21 } = 2.83 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 9 }{ 2 * sin 26° 31'31" } = 10.08 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 14**2+2 * 19**2 - 9**2 } }{ 2 } = 16.07 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 19**2+2 * 9**2 - 14**2 } }{ 2 } = 13.115 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 14**2+2 * 9**2 - 19**2 } }{ 2 } = 6.946 ; ;
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.