5 21 22 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 21   c = 22

Area: T = 52.30767873225
Perimeter: p = 48
Semiperimeter: s = 24

Angle ∠ A = α = 13.08773526646° = 13°5'14″ = 0.22884173944 rad
Angle ∠ B = β = 71.99655469999° = 71°59'44″ = 1.25765593419 rad
Angle ∠ C = γ = 94.91771003355° = 94°55'2″ = 1.65766159173 rad

Height: ha = 20.9232714929
Height: hb = 4.98215987926
Height: hc = 4.75551624839

Median: ma = 21.36600093633
Median: mb = 12.01104121495
Median: mc = 10.58330052443

Inradius: r = 2.17994494718
Circumradius: R = 11.04106321925

Vertex coordinates: A[22; 0] B[0; 0] C[1.54554545455; 4.75551624839]
Centroid: CG[7.84884848485; 1.58550541613]
Coordinates of the circumscribed circle: U[11; -0.94663399022]
Coordinates of the inscribed circle: I[3; 2.17994494718]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.9132647335° = 166°54'46″ = 0.22884173944 rad
∠ B' = β' = 108.0044453° = 108°16″ = 1.25765593419 rad
∠ C' = γ' = 85.08328996645° = 85°4'58″ = 1.65766159173 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 = 5 ; ; b = 21 ; ; c = 22 ; ;

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

p = a+b+c = 5+21+22 = 48 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 48 }{ 2 } = 24 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24 * (24-5)(24-21)(24-22) } ; ; T = sqrt{ 2736 } = 52.31 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 52.31 }{ 5 } = 20.92 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 52.31 }{ 21 } = 4.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 52.31 }{ 22 } = 4.76 ; ;

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{ 5**2-21**2-22**2 }{ 2 * 21 * 22 } ) = 13° 5'14" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-5**2-22**2 }{ 2 * 5 * 22 } ) = 71° 59'44" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-5**2-21**2 }{ 2 * 21 * 5 } ) = 94° 55'2" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 52.31 }{ 24 } = 2.18 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 13° 5'14" } = 11.04 ; ;




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

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