19 21 29 triangle

Obtuse scalene triangle.

Sides: a = 19   b = 21   c = 29

Area: T = 199.2621605685
Perimeter: p = 69
Semiperimeter: s = 34.5

Angle ∠ A = α = 40.87333755385° = 40°52'24″ = 0.71333749796 rad
Angle ∠ B = β = 46.32553388901° = 46°19'31″ = 0.80985296907 rad
Angle ∠ C = γ = 92.80112855715° = 92°48'5″ = 1.62196879833 rad

Height: ha = 20.97549058615
Height: hb = 18.97772957795
Height: hc = 13.74221797024

Median: ma = 23.46880634054
Median: mb = 22.15328779169
Median: mc = 13.81112273169

Inradius: r = 5.77656987155
Circumradius: R = 14.51773476348

Vertex coordinates: A[29; 0] B[0; 0] C[13.12106896552; 13.74221797024]
Centroid: CG[14.04402298851; 4.58107265675]
Coordinates of the circumscribed circle: U[14.5; -0.70994944333]
Coordinates of the inscribed circle: I[13.5; 5.77656987155]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.1276624462° = 139°7'36″ = 0.71333749796 rad
∠ B' = β' = 133.675466111° = 133°40'29″ = 0.80985296907 rad
∠ C' = γ' = 87.19987144285° = 87°11'55″ = 1.62196879833 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 = 19 ; ; b = 21 ; ; c = 29 ; ;

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

p = a+b+c = 19+21+29 = 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 * (34.5-19)(34.5-21)(34.5-29) } ; ; T = sqrt{ 39705.19 } = 199.26 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 199.26 }{ 19 } = 20.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 199.26 }{ 21 } = 18.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 199.26 }{ 29 } = 13.74 ; ;

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{ 19**2-21**2-29**2 }{ 2 * 21 * 29 } ) = 40° 52'24" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-19**2-29**2 }{ 2 * 19 * 29 } ) = 46° 19'31" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-19**2-21**2 }{ 2 * 21 * 19 } ) = 92° 48'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 199.26 }{ 34.5 } = 5.78 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19 }{ 2 * sin 40° 52'24" } = 14.52 ; ;




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

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