3 19 21 triangle

Obtuse scalene triangle.

Sides: a = 3   b = 19   c = 21

Area: T = 22.29877016753
Perimeter: p = 43
Semiperimeter: s = 21.5

Angle ∠ A = α = 6.41772389321° = 6°25'2″ = 0.11220019483 rad
Angle ∠ B = β = 45.06113522925° = 45°3'41″ = 0.78664689629 rad
Angle ∠ C = γ = 128.5211408775° = 128°31'17″ = 2.24331217424 rad

Height: ha = 14.86551344502
Height: hb = 2.34771264921
Height: hc = 2.12435906357

Median: ma = 19.96987255477
Median: mb = 11.60881867662
Median: mc = 8.64658082329

Inradius: r = 1.03771024035
Circumradius: R = 13.42106656972

Vertex coordinates: A[21; 0] B[0; 0] C[2.1199047619; 2.12435906357]
Centroid: CG[7.70663492063; 0.70878635452]
Coordinates of the circumscribed circle: U[10.5; -8.35884847763]
Coordinates of the inscribed circle: I[2.5; 1.03771024035]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 173.5832761068° = 173°34'58″ = 0.11220019483 rad
∠ B' = β' = 134.9398647707° = 134°56'19″ = 0.78664689629 rad
∠ C' = γ' = 51.47985912246° = 51°28'43″ = 2.24331217424 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 = 3 ; ; b = 19 ; ; c = 21 ; ;

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

p = a+b+c = 3+19+21 = 43 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 43 }{ 2 } = 21.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21.5 * (21.5-3)(21.5-19)(21.5-21) } ; ; T = sqrt{ 497.19 } = 22.3 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 22.3 }{ 3 } = 14.87 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 22.3 }{ 19 } = 2.35 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 22.3 }{ 21 } = 2.12 ; ;

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{ 3**2-19**2-21**2 }{ 2 * 19 * 21 } ) = 6° 25'2" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-3**2-21**2 }{ 2 * 3 * 21 } ) = 45° 3'41" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 21**2-3**2-19**2 }{ 2 * 19 * 3 } ) = 128° 31'17" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 22.3 }{ 21.5 } = 1.04 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 6° 25'2" } = 13.42 ; ;




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

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