7 19 21 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 19   c = 21

Area: T = 66.04768583659
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 19.3333244003° = 19°20' = 0.33774287629 rad
Angle ∠ B = β = 63.97442200559° = 63°58'27″ = 1.11765607764 rad
Angle ∠ C = γ = 96.69325359412° = 96°41'33″ = 1.68876031143 rad

Height: ha = 18.87105309617
Height: hb = 6.95223008806
Height: hc = 6.29901769872

Median: ma = 19.71767441531
Median: mb = 12.44398553046
Median: mc = 9.7343961167

Inradius: r = 2.81105046113
Circumradius: R = 10.57220395682

Vertex coordinates: A[21; 0] B[0; 0] C[3.07114285714; 6.29901769872]
Centroid: CG[8.02438095238; 2.09767256624]
Coordinates of the circumscribed circle: U[10.5; -1.23220797993]
Coordinates of the inscribed circle: I[4.5; 2.81105046113]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.6676755997° = 160°40' = 0.33774287629 rad
∠ B' = β' = 116.0265779944° = 116°1'33″ = 1.11765607764 rad
∠ C' = γ' = 83.30774640588° = 83°18'27″ = 1.68876031143 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 = 7 ; ; b = 19 ; ; c = 21 ; ;

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

p = a+b+c = 7+19+21 = 47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 47 }{ 2 } = 23.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23.5 * (23.5-7)(23.5-19)(23.5-21) } ; ; T = sqrt{ 4362.19 } = 66.05 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 66.05 }{ 7 } = 18.87 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 66.05 }{ 19 } = 6.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 66.05 }{ 21 } = 6.29 ; ;

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{ 7**2-19**2-21**2 }{ 2 * 19 * 21 } ) = 19° 20' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-7**2-21**2 }{ 2 * 7 * 21 } ) = 63° 58'27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 21**2-7**2-19**2 }{ 2 * 19 * 7 } ) = 96° 41'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 66.05 }{ 23.5 } = 2.81 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 19° 20' } = 10.57 ; ;




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

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